Hi Tom welcome to the forum you'll find the members on here are a friendly and helpful bunch. I'd recommend you search eBay but include international sellers. This is what I'm now having to do with my 21 year old a6 c5.
Solenoids can be a problem or the module. However the first thing I'd look at is when was the gearbox oil last changed?
Degrading/old oil can affect the gearbox to change gears effectively.
If you bought it from a dealer within the last 30 days I'd recommend you take it back for them to repair. They should repair this foc. It could be an issue with the pollen filter housing or clogged battery tray holes.
I might be going, but I haven't got a ticket booked as I was just going to turn up on the day. I won't be in my Audi though as it's off the road needing an engine rebuild.