Evelynmoo there is more flexibility with medicated fet so yes if the lining isn't right they would wait and do another scan. My clinic though has you sign, if lining above 6mm then transfer will be scheduled (about a week later).
Also means the bloods aren't quite as urgent as they schedule your transfer you don't ovulate on medicated so they aren't testing to make sure they catch ovulation. They just transfer when the lining is right. I have no idea if this can go for weeks or whether there are still some time restrictions but my fs said we can schedule transfer and u/s to suit us, within reason!
I hope you have some luck with your fs, I can't see why trying medicated wouldn't be a good idea. It may make a difference???!!!