These two things seems rather at odds with each other. On one hand, you're talking about the masters having an advantage because they can choose who will get the bonus next war, on the other you're talking about them being at a score disadvantage.
Masters had a big score disadvantage during the last Trials. You had to pretty much ace the War and Masters' tournament to get as many upped cards as the top challenger.
There's also the whole thing where it rewarded you for helping a team to do well. Let's say that Sir Valimont wanted to try out for entropy master. For what I can tell, he was every bit as important to entropy's victory as Zeru, but he gets no bonus for it, which hardly seems fair.
General is a leader of a team, so naturally if one person gets rewarded, that person will be the General. Even if some other team member worked harder, it was the General who picked that team member during the Auction.
Rewarding the whole team would be nice, but it cannot be done because of the reasons I explained earlier.
Additionally if all someone wanted was to be master, it would actually be to their advantage to throw the war, so that the master wouldn't get any bonus either. This problem seems to be at least as large as the one you're trying to fix.
Me as a General
not bidding on Frank and taking someone else (equally qualified) from the huge available player pool, is a very simple process that takes zero of my time and gives me no real disadvantage in War. Best part is that there's no way of getting caught doing this because I don't have to give reason why I don't bid on a specific player.
Frank joining my team and spending
two months sabotaging battles in order to deny me from getting 1-5 extra upped cards during Trials (which I might not have even got without the sabotage), would be pretty ridiculous. Frank would choose those couple of upped cards over the possibility of being the winner of the biggest PvP event of our community, while at the same time killing his own reputation by letting everyone think he sucks in PvP.
See the huge difference between those two?
My other option was to get rid of War bonus altogether, but I think War bonus a nice way of motivating the Generals to perform better during the War, without giving them any huge advantage over the Challengers during Trials. Previous bonus was a big one, but now that I cut it in half, it's not that important anymore.