Changing compounds would be a disaster and make the series gimmicky and seem more like "Whacky Races". If you were to equate F1 tyres back to the LFS nomenclature then if prime is R3 then the option would be R2.6 or R2.7.
R2 are qualifying tyres for FO8 now. R3 and R4 would be less ridiculous, but there would still be no strategy in it as you would just run R4s for the shortest possible period.
As for the warmup lap - we tried that in OWRL F1 and it didn't really serve the purpose. Tyres were not warmed significantly and there are all the disadvantages (warmup lap crashes, drivers in wrong order, no native jumpstart penalty).