I would NEVER take a Supra to a main dealer unless it was a mint stock car and I wanted original parts and to maintain a Toyota service history
You will see the final bill climb well beyond £300 IMO, it is easily done at a £95 per hour rate (especially when they then add VAT!!)
Sorry to here this though, I have always used Elite in Rainham, they are specialists in this field as are Wheels In Motion etc, if they come across an issue they also ask before continuing to rack up the invoice cost
The other issues is that a VW dealer is unlikly to have parts to hand and replacments will be via a 3rd party and expensive
Lessons learnt and all that is all you can put this down to, hope you are happy with it when it comes back anyway