I got my MS online - How do I ask profs for a LoR?
Given that every encounter you've had with your professors thus far has been online, I would suggest just biting the bullet and e-mailing asking for that letter of recommendation. I presume you built a rapport up with them during your masters programme? You could even say that you look forward to finally meeting them at the conference.

I don't think you need to worry about it particularly given, from what you said, you've done well in coursework and actually achieved the Masters. Don't worry about it, after all, the worst they can say is no, and that's very unlikely.

As for the research project: go and smash it and get yourself another recommendation so you can move confidently into a PhD programme!