Why would she not have sex with you on her period? Is she an orthodox Jew or what? If she is an orthodox Jew, how come she is having sex outside of marriage?... Weird.

The involvement of the friend, the BPD, etc. are all very difficult emotional issues that would be hard to resolve, but the practical issue of " but don't have the time for sex more than once a week, and that is if she isn't on her period. " - the issue that results in having sex three times a month rather than four times a month, i.e. a 25% loss - is easy to resolve by having sex on her period. If she does not like the mess, she can use a tampon. Having sex on her period would be beneficial to her if she has cramping during the period - many women do. So there might even be a collateral benefit to that practical change.