I played around with getting past the blackout last night with my AtBat account from the T-Mobile promotion. I ended up getting it to work but it was a little bit of a headache.
Private Internet Access is my normal VPN. I couldn't get it to work at all. If I was connected to any of the servers in the US it wouldn't play. It gave a generic error that wasn't very helpful in letting you know why. If I connected to any of the foreign servers I couldn't even log in. I have something to try with this scenario now.
When PIA didn't work I gave Adguard's VPN a shot. They have a limited free version of it so I figured "Why not?" At first it looked like it was going to have a similar issue to PIA's foreign servers. I couldn't log in. So I tried turning it off, logging in, and then connecting and that worked! The stream played. So it looks like they're an option.
I'm going to try tonight with the PIA foreign servers using the same login trick. I'm hoping that gets around it. It seems like MLB has recorded the IPs of the VPN servers and are blocking them. If that's the case then using a smaller provider is going to be the best bet. It might be a little bit of a wack-a-mole game though on which servers work.
This is on a desktop btw and not a phone. Phones are a whole other headache. The app is using the GPS and known wifi and cell towers to get your location and not relying on an IP geo lookup. I'm not even going to try to get that one going right now.