Personally, I’d say to go pretty light on the trail centres and do as much natural stuff as possible as to me, that is where Scottish riding is at its best.
Highlight regions to consider as a base are Kinlochleven, Braemar, Aviemore and Torridon. You could easily spend 4-5 days at each and not ride everything worthwhile nearby. Each has several challenging ‘big’ days out, at least one good 2 day tour plus simpler days within pedal or a short drive.
If you really feel that you have to do trail centres, do either Glentress/Innerleithen or Dalbeattie/Kirroughtree.
Laggan is handy for both Ft Bill, Aviemore or the road north to Torridon, so can be fitted into a road trip quite well.
Anytime from late April to mid June can be superb, and generally midge-free. Later in September and the first half of October can also be superb (this year was the best for a long time…) but so long as you accept the risk of some mixed weather, anytime from 1 April to 1 November is good.