I must say that MC breaking the ice princess image so fast was dissapointing, and wasn't even on purpose by using his game knowledge.
The whole thing about him loving her firm persona and she only melting after many interactions...gone.
I fear MC trainging them and making them too strong could change the plot, at the same time it shoudl make them ahrder to kill, unfortunately they are really in a position that one will die for the other one to live, with the most realistic outcome with both living being princess runs out from the country and -not-Kallen to go in hiding if things go bad.
There is even how MC is probably suspect, he acts with too much sass on the Knightmare, when a native of Japan should have no experience, someone with some brain would wonder how a random civilian can pilot on a pro level without training.