There's quite a big difference between armed merchant ships and privateers and "top of the line warships" -- the entire United States didn't have anything that even remotely resembled a top of the line warship until way, way after the time of the Founding Fathers. Even the vaunted 'super frigates' weren't even close to being a ship of the line.
As for militia artillery, those were expensive and typically purchased by towns as a whole for the use of the local militia, not privately owned by a single person. So the historical precedent on those can fairly said to be grey. It's quite clearcut for small arms, but beyond that less so.
I would say you're splitting hairs on warships, there's quite a big difference in
firepower, but absolutely none in terms of
legality. There's absolutely no reason to think the US government, which was good with entire privately owned artillery regiments, frigates, and would suddenly say "Oh my, we were good with 24-pounders but these 30-pounder cannons on your privately owned ship are just too much, we better not have these in private hands."
As far as militia artillery being publically owned by towns, you're just plain wrong.
Most fur traders packed at least one cannon on their riverboats for fighting off indian attacks.
We also have numerous examples of private ownership, often in bulk. F'rex we have receipts and records from that era showing that Simeon Potter personally owned ten cannons and ten swivel guns, and that Ephraim Bowen negotiated to purchase some from him for the Continental army.
In another letter, Colonel John Glover assured a man that if the two cannons the man loaned him were lost, Glover would reimburse him to the tune of four hundred pounds.
That's beyond the numerous privately owned artillery companies and regiments, like Gale's Independent Company of Artillery, The Artillery Company of Westerly and Charlestown, or Smith's Artillery in Maryland. And, well, again the Privateers with estimates going up to 2000 privately owned warships.
