Ouch, that is going to sting, and I feel for you... facing having to spend almost 50% of the worth of the vehicle to repair it is galling to say the least
Who diagnosed it, out of interest? If it was an Audi dealership, then there may be a chance you could still repair rather than replace, as they immediately trotted out the "6 grand to replace" approach on my old A4... they are always big fans of replacing everything rather than spending time troubleshooting and only replacing what is necessary. Did they drop the fluid from the box and find horrible metal shavings, or was it just a case of PRNDS on the dash and "computer says no"?
If you can speak to an actual specialist who knows about repairing multitronics (see my other reply), they may give you an idea of whether it may still be repairable. If it is just the controller, you may get away with a bill of only £1K rather than 6! Being undriveable makes things more of a pain, as you can't just pop elsewhere for a second diagnostic, but trucking it a few hours away and repairing is still going to be cheaper than a new box.
When my multi crapped out, it opened my eyes bigtime, and I ended up doing a lot of research, and then traded up for something with a much better reliability record.
Whatever course you decide on, I can offer this: If it were me, and it were repairable, I would fix it and then
get ****** rid of it! If a replacement was the only option, I would go with reconditioned, and then consider very seriously
getting ****** rid of it!