FWIW, it would be handy to use an older calendar, so we wouldn’t have to deal with the lack of a year zero and those pesky negative years...
I'd have no particular issue with using a Jewish calendar. It goes back far enough that negative dates aren't really a problem.
If you're going to use a modern calendar system though, using BCE is silly, as it begs the obvious question as to what exactly the defining event that it refers to is.