Hi there.
I think the shower thing is a pretty good idea, but the only issue I see is that it can't be done long term...there's no feasible way to shower with him every time before sex.
I will confess I don't know enough about borderline to factor that in to his responses, so please bear that in mind. The best I could suggest without directly bringing it up would be to either relate a "story a coworker/friend/yourrelationhere told you" about an ironically similar situation (wink wink), and hope that he takes the memo. Otherwise, the best thing to do is I would think to, as politely and nonjudgmental as you can explain that, while you enjoy what you have with him and you love him very much, that it's necessary for you that he clean himself a little more thoroughly. It might not hurt to point out that he'd expect the same from you. That, I think, is the best way to go.
I wish you both the best, and good luck.
Hugs,
Harley