You want 300s if you're dealing with standard engines. It gets you max payload for 3/5, 4/6, and 5/8 mechs, 3/5 tanks, and 5/8 and 8/12 ASF and is a step short of max 7/11 ASF.
For XLs, though, it's only max payload for for mechs at 3/5 and 10/15 and for ASF 12/18 and 5/8. Higher rated XLFE will hit at or near the optimum weights for more useful mid-range movement profiles. The 360 is generally considered the most flexible for ASFs, but divisibility by 25 is more valuable for mechs if you are tolerant of relatively slow XL mechs and by 7 if you're particularly intolerant of them which make the 350 a candidate.
340s lack useful factors and can only go in 85 tonners at 4/6 for mechs 6/9 for ASF. When you're talking about altering one of a very small number of XLFE lines the Lyran Commonwealth has that's not ideal. I'd look at doing an even more ambitious heavy cavalry Warhammer with a 350 or look into up-engining the Chippewa with a 360. The latter gets almost everything they wanted from the Orca.