Can steam support help with transfering a game?

Pretty sure they wouldn't want to transfer the game.

Even if they could (probably), and even if they would be willing to (doubtful), by the time they got around to processing your support ticket you could have bought the game again with spare change you found on the street. :P

No. You'll have more luck buying it yourself.

in my experience, they will just tell you to use Steam Family Share and refuse to do anything. You could try though. You should buy a copy of the game to activate on the Steam account associated with your SG account to avoid trouble.