Also, the strong-willed characters (Kai, Kyosuke for example) gain morale faster by getting hit instead of evading. Then there are those who lose morale by getting hit, those who do gain only by evading, etc.
Unless you already have an idea of the pilot mentality via OGs/OG Gaiden, I guess the safest way is just to feed those you want to gain morale kills.
Currently playing: Bravely Default Flying Fairy (3DS), Tales of Xillia 2 (PS3)
later on you're generally given enough grunts to deal with that everyone will hit the morale cap regardless of who kills who, but for now you either have to have your MB squad go for the kill, get them a skill like morale+2 at the start of every turn, or burn SP on seishins to do the job.
edit: and yes you're right, all four MB units need 140+ morale
There's a whole bunch of skills dedicated the acquisition of morale. Never been a better time to consider using them (in particular, I found Morale very handy for Tetsuya, who often came up shy of being able to contribute the Tronium Buster Cannon).
The problem with the other morale gain skills is that they require the units to be in the thick of things, but with morale +destroyed, your units will always be getting that extra morale. For your situation, I think it'd fit perfectly. Being only 100PP, you could always replace it late game as well if you simply end up spamming rouse.