Like others, I've had some trouble getting the remastered versions going, but it's now working in windowed mode. The thing is, I don't want to play through the full game like that, and I don't want to sink more time into workarounds like borderless, particularly with the risk of crashes.

My current plan is to wait until the classic versions are released, but I've been dying for these to be released on gog and would love to start playing today.

Does anyone know if the save games from remastered are compatible with the classic version? Can I just copy them across from Documents\BioshockHD to Documents from Documents\Bioshock and pick up where I left off?

According to this: https://steamcommunity.com/app/409710/discussions/0/350542145691582635/

it does not work when you import the old savegames to the new version. This probably means it will be the same the other way round

They're not compatible as they're made in different engines (Classic = Unreal 2, Remastered = Unreal 3). I'm waiting for GOG to get the Classic versions too.