Should I ask to work on professor's project?
Yes, you should ask! Don't be shy -- there's nothing at all to lose. In the worst case, he'll point out that the logistics of collaborating remotely are hard, or something like that. No one is ever upset that someone is enthusiastic about working with them. If you're worried about the lost opportunities of doing research with someone more local: having a project you like and an advisor you work well with seems far more important than local convenience here -- it's not like you're in a field that needs a lab and hands-on training.