I can't speak to the seller experience, but I have bought 2 vehicles from BAT - a '57 Cameo pickup and a '49 Cadillac Sedanette. I had good experience with an orderly process both times. In both cases, I used BAT shipping which seemed to be pretty seamless. I also used the BAT check out process on the Caddy, which I liked because they certified the title and final delivery before releasing funds to the seller (partial on receipt of good title, remainder on delivery).
I know auctions are always a risk and "caveat emptor" is the rule of the day, but I've had good luck (knock on wood) with both BAT and the 2 cars I have bought at Barrett-Jackson.
Good luck with your sale!