We don't have to assume Congress would approve a military in 1920 because in 1919 said force already existed; total U.S. Armed Forces strength in 1919 was 1,172,602 of whom 851,624 were U.S. Army. They did do further demobilizations in 1920 but that was in the context of a peace time situation, which wouldn't hold here because of the obvious war situation. It's also worth noting this war wasn't "out of the blue" but had bipartisan support and was being aggressively pushed by the Republicans who were ascendant in Congress, with Senator Fall being a Republican. To quote from Woodrow Wilson and the Mexican Interventionist Movement of 1919:
From mid-November until the reconvening of Congress in December, the related crises deepened. Jenkins, advised by Matthew Hanna of the state department, refused to pay the nominal bail set by the Puebla court and called upon the United States government to secure his freedom. Lansing responded by sending strong notes to the Carranza government urging it to release Jenkins immediately. When the Mexican Foreign Office reminded Lansing that in a federal republic the central government may not interfere with state jurisprudence, the secretary was angered.62 He held a stormy interview with Ambassador Bonillas on November 28 and threatened that, if Jenkins were not released immediately, a "tide of indignation" among the American people might prevent further diplomatic discussion and force a break in relations which would almost inevitably mean war 63 On the next day Lansing sent the Mexican Foreign Office a harsh, insolent note containing a peremptory demand that Jenkins be released immediately. Although he had not heeded Fletcher's advice of November 21 to give Carranza forty-eight hours to free Jenkins or have the United States sever diplomatic relations, Lansing had taken strong action. The sending of the peremptory demand to an apparently unyielding Carranza government had moved the two countries to the brink of war.The Republican controlled Senate responded favorably to Lansing's well-publicized initiatives. After conferring with Fletcher at the state department, Senator Brandegee wired Fall to postpone his subcommittee's investigations in the West and return to Washington, because no action could be taken without him. On December 1, state department officials met Fall at the train station and drove him to Lansing's home. Following a pattern set in mid-November, Lansing gave Fall copies of his diplomatic correspondence with Mexico; and the two men discussed the Mexican crises. Lansing explained that he was acting on his own initiative without the knowledge of President Wilson. Fall told Lansing that his subcommittee would make an official report to the Senate and that he would introduce a resolution upholding Lansing's hand.65
As far as Leonard Wood goes, he was viewed as a conservative by 1920 as a result of his intense Anti-Bolshevism and Americanism stances.
It would be fatal, because how else can an insurgency survive without weapons and munitions? The Mexican Revolution was possible because of entities like the United States and German Empire funneling weapons into the region, while the Mexican factions themselves held the cities and thus means of producing their own equipment but neither possibility exists here. Numbers, motivation and experience are all well and good, but they don't produce effective results in the fields without the industrial capacity to back them up; see the German Army in 1945 for a good example. Likewise, the Zapatistas did find their support in the agrarian areas but they also lost said Mexican Revolution and ended up having to make peace with the Mexican government, so I fail to see why they would be more successful against a more powerful opponent.
As for the Banana War conflicts, yes, the U.S. had to fight an anti insurgency campaign for years; I see the same happening here with Mexico. That doesn't detract from the fact, however, that American willpower failed to break and in the end the U.S. was able to enforce its political desires. Just as you've pointed out Mexico had experience with both irregular and conventional warfare, so too did the United States but also a force size and industry many times over that than what Mexico possessed. The 400,000 troops the U.S. could use in the conventional phase of the conflict is nearly twice as large as what any side in the Mexican Revolution could deploy, for example.
I've touched on it earlier, in that this is why I think a long standing occupation is likely. There is no ready alternative to the existing order available for the U.S. to use, so they will have to build one from scratch the same way the United States had to in both Iraq and Afghanistan in modern times. The motivation is certainly there, because it would be obvious to Washington that a withdraw would result in a hostile government coming into power on the southern border, an intolerable national security threat.
Such ignores the specific political circumstances unique to 1919, however, namely that the First Red Scare was going on and still intense at the time before gradually declining in fervor over the course of the 1920s. There was also nothing comparable to the situation faced in 1919, in that isolated attacks on personal property did not threaten American economic interests the same way nationalizing the extremely large and profitable holdings held in oil did, nor did murder or kidnapping of Americans occur in such a way as the Jenkins Affair, which also broke international standards with regards to diplomats. An American citizen paying a fatal price after willingly taking personal risk is one thing, but attack an American official and than having the Mexican Government arrest him on allegations he planned his own kidnapping is quite another.
See what I said earlier about the changed politics, but also the situation of Garrido's rise and American investment in Mexico. The U.S. trusted the wider government by that point and didn't have a vested interest in their agricultural sector like they did in the energy sector.
Basically, and no disrespect intended, your argument boils down to Will to Power based on Nationalistic desires. It's understandable position, but it isn't reflected well in the real world; could one say the Filipinos, the Central Americans, Caribbean peoples, or even Native Americans were less motivated? How about the Germans and Japanese in World War II? Motivation to fight is an important factor, but it isn't, on its own, decisive in Insurgency contexts. Even the Iraq War, despite its unpopularity, saw the U.S. willpower last long enough to install a government that still to this day more or less stands in control of Iraq. Unlike said conflict, however, the U.S. would and did have a lot of motivation to fight a war in Mexico in the timeframe.
If we're assuming that a President Wood goes for an invasion of Mexico then the important date isn't 1920 but March 1921 as that's the 1st point he has any real power. Coupled with the impact of WWI and the pandemic as well as the paralysis and division resulting from Wilson's ill health and mismanagement I think its reasonable to ask whether the US would still have the deployed manpower and the will - both by the government, public opinion and probably also the conscripts being sent into this new war zone.
In terms of how long an insurgency last that depends on the level of motivation. If your talking about a prolonged occupation by a foreign invader who is probably behaving badly and also looting resources that could be quite a while. Mexico isn't a 1st rate power at this time but its not a pre-industrial one either. It doesn't take much to produce some basic guns, or for the matter steal/buy from the occupying forces. After a year or two with prolonged bloodshed and heavy occupation costs how attractive will this be to many Americans? The forces involved in assorted Caribbean or isthmus nations were quite small and a hell of a lot more will be required for occupying Mexico. Other when at war the US maintained only very small military forces in peacetime until 1945.
The Philippines have been the only time before 1945 when the US occupied a sizeable nation and while successful US actions there received a lot of criticism. This is likely to occur again here, especially since the operation is even larger and a lot closer so reporters and others can gain access to details.
You mention US successes in Iraq but isn't the current government largely dominated by the Shia groups, many of whom are close to Iran. In Afghanistan the US is pretty much giving up on opposing the Taliban. Although there's a chance that Biden may change this US will to continue with no clear end is sight is waning. That's despite this being a pretty low level operation and the US having substantial support from both allies and internal groups.
Its possible that the US can impose a new regime but how likely is that to last once they withdraw? Or are they going to return every time their strongman is deposed or threatened?
Steve