After the transfer aborted I was locked in a loading screen for more than a minute. After closing the game and reopening, the green eyeball was still open. Mousing over it, it offered to send me into the brawl. I clicked yes, to see what would happen. Again I got stuck. Again it gave me the option of entering the brawl.
In a previous training grounds a few minutes earlier, I didn’t notice a transfer aborted, but was locked in a loading screen. That time, after closing the game and reopening, I was able to enter the correct instance.
Edit to add: I could not requeue because the system was telling me I had recently queued for a heroic dungeon.
Edit to add: I’ve had several more times when I had to close the game and restart it in order to enter a training grounds bg whose loading screen I got stuck in. The last time that happened I later started to dc, quick closed the game and logged back in, at which time I had a deserter debuff.
I guess that’s one way for Blizzard to milk more time out of players.