Alright, I've had my wrists slapped a couple of times by bringing up high speed sync, but I'm gonna keep experimenting because it costs me nothing to do so.
If one can use ISO 1600, SS 1/500th and f/2.8 without flash, then why not try HSS to either reduce ISO 1600 to 800, SS to 1/1000th or aperature to f/3.2? It seems to me that any extra light thrown on the subject is worthwhile.
Here are a couple of HSS-flash photos from a 7th-grade game last week bounced off the ceiling in the darkest venue that I have been in this season:
#1 Rebound after boxing out
#2 You can't block my shot if you are laying on the floor down there.
It seems to me that one doesn't need to be a purist to get something that might work.
OK, flame me, I'm ready for it!