Out of these recommendations Code Geass is simply the best. For anyone reading here is a pitch:

The Holy Britania Empire which is the America of this alternative world (which were British settlers and the way the invaders treat the Japanese has too many parallels with Japan under US occupation). There is our protagonist who is a genius and this genius creates a sovereign country out of a borrowed room from the Chinese embassy and expands it to the point of taking down the Holy Britania Empire itself. There are also really good mech battles.

No convenient plot moments. No Deus Ex Machina. No pulling punches. No need to suspend the disbelief. It's just a guy who takes on an Empire with country of his own which is a borrowed room.