After the great advice from Firo (many thanks Fiona) I contacted Koray and Gunes re: selling quad (to another yabanci). We did do it without any kimlik no. Gunes phoned a notary office (won't mention which number) who told her my tax number didn't exist (where's all the tax I've paid gone?) Luckily she had the forsight to phone a different notary who said there was no problem re: tax no OR selling/buying. That was notary no. 1. Very helpful.
Downside is you (as the purchaser) do (apparently) have to go to Mugla for re-registration. Seems like they're bringing in this new bit about the plaka being yours not the vehicles. That is what the notary told us. However, you can pay some traffic 'person' to do it with power of attorney.
So, it is possible, definitely would suggest contacting Koray and Gunes who really went out of their way to help. Many, many thanks to you both
PS That was a total waste of 650tl for residency[
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