I know you said you were not using BT for the 'Mech combat, but I actually was in a moderately successful MechWarrior PbP (moderately successful as in we got though two entire 'Mech scenarios before the game dissolved sometime in the third) where we just used straight up BattleTech rules, only we used the Dueling Rules from MaxTech.
The Dueling Rules let everybody take their turn all at once, not unlike a traditional RPG, instead of repeatedly cycling back and forth between sides multiple times per turn. The major downside is that, unlike most RPGs, everybody absolutely must wait for their turn in the Init sequence to come up, instead of just lumping it into the common PCs go-enemies go mode that frequently occurs.
Just throwing it out there.