Lol my mother was *obsessed* with initials when it came to me naming my kids (funnily enough mine are DLR, which makes no sense at all, so I don't see why she was so adamant about what my kids' initials would spell, if anything).
I think JAM or JIM are fine - initials I would have a problem with would be something like Fiona Amelia Thompson or Catherine Olivia Williams, kwim

'Jim' would be a pretty cool nickname for a girl I reckon, I'd give my child those initials *just* so I could call her Jim hahaha

I think the names you have chosen are beautiful. Go for it!!