if his plan for that test needed Lynn (or someone on his level) in the same way that she needed him for the STIC, then the operation wouldn't happen if she's not in and he leaves money on the table (the subs say the plan 'requires' her). i mean i guess he could look for other people but he would probably see it as easier/less time-consuming to try to guilt someone he's already familiar with and knows is competent.
i do think he feels that level of desperation though. the way he sees it, his life is over because the path to success he was envisioning for himself is gone. expelled from school, probably some kind of record, i'm not even sure if he would be allowed to take that test himself in cases like that. the academic path to success is closed off for him so he needs to feel like he needs to pendulum shift to the other direction because he needs to start all over anyway.
i also don't think his mother is a big part of the reason anymore. I imagine the scene where Lynn first gets caught for cheating and the principal criticizes her dad for not raising her right and he later gives back the shirt she bought for him but like 10x that for Bank's situation. and i think the principal scene and the shame Lynn's dad feels is a good indicator to how Bank's mom would feel. that whole thing was on an international scale. who knows if she's around. maybe that's why the name change.