If your kid is used to getting up early, the best strategy for avoiding crowds at Keystone is to get there at first lift and jet straight to the Outback. Go to River Run and if the gondola line is backed up you can usually get to the top faster by walking across the bridge to the Summit chair-- they both go to the same place. Don't bother with the second gondola; bomb down Mozart (or better yet Diamondback if it's open and they groomed it). You'll get to Santiago chair when it opens. Take that up and hit Anticipation and you'll get to the Outback before the second gondola people. The Outback will eventually crowd up, but you are there before 9 and it will be quiet for a while until the goobs wander over. When they do, start making your way back to the front side, which will be against the flow of the mob. Go to the Mountain House for a late lunch. Not as scenic and a lot older compared to the Outpost, but you mentioned avoiding crowds. The Outpost is elbows out, trays up. Afternoon, if your 10 y.o. is up for it and your legs hold up you can make another trip to the Outback, it should calm down by then.
I don't think A-Basin should give you too much of a problem with crowds. They're getting a lot of their terrain open early this year, and should have all their lifts spinning (including the new one) which is extraordinary for this time of year. Just avoid the Black Mountain Express lift and you should be good. But again, get an early start. They have the same number of parking spaces they had when the ski area was half the size and it fills up fast.
Have a great trip!