I suspect the code you'll see is 'output speed sensor implausible' or 'incorrect gear ratio', both of which require a rebuild. At this point I feel its pretty unlikely to be the F125 as that will throw a code as you select a gear, not when you try to move. What I think has happened is that it has blown the end off the 'A drum' thusly:
The bang when it does try to move is the TCU not getting the result it expects (movement) and just going 'f it' and throwing it in 3rd with full line pressure. If it reverses then it has enough fluid to drive the torque converter and clutches etc so I think its unlikely to be a fluid level issue.
At this point its going to make no difference to drive it in limp mode so I'd just drive it the 8 miles and see what they can come up with. Do they have VCDS or a generic scanner? If its a decent generic like a Snap-on it may tell you what the actual problem is. If its a cheapo handheld which just gives Pnnnn OBDII codes tbh its pretty much worthless. It would be more effective to post you my VCDS cable since I can live without it for a couple of days.