Finally checked out Auto Sales Park Auction (AutoSalesPark · Pinson Valley Auto Auction, Inc.) (Birmingham, AL) after seeing their lot on my commute for months. They keep around 89 vehicles, mostly family SUVs and sedans. They were totally fine with my mechanic doing a once-over, which honestly settles half the trust question.
Lot address: 5193 Pinson Heights Rd, Birmingham, AL 35215. Visitor parking: Yard parking at Pinson Heights Rd; downtown office 1901 6th Ave N #3100, Birmingham, AL 35203. Website: https://autosalespark.com. Board status: verified / trusted dealer.
Paper side: licensed with the state (looked it up), about 98% of stock has title in hand per the office, and they offer a 30-day/1,000-mile powertrain warranty.
Overall: decent cars, pushy back office. The $399 doc fee is fine but watch the add-on sheet — say no twice and the price comes back to earth.