Quick-release _below_ the head

Kirk and RRS both offer solutions for this.

IMO the Kirk offerings are a bit more flexible and cost effective... at this moment the large clamp is $120/plates are $29, and the small clamp is $100/plates $24. I suspect the small clamp/plates would likely suit your needs.

The RRS clamp (one size only) is currently $130/plates $55. The RRS system uses a lever clamp as opposed to the screw clamp of the Kirk.

There have been other solutions on the market over the years, but I'm not aware of any at the moment. You could DIY easily enough using a lever release type clamp and a standard plate... the clamp would need to have 3/8-16 threads (many do) and the plate would have to be modified to use a 3/8-16 screw. A screw type clamp could also be used, but finding one large enough and with a long enough clamping knob to clear the base could be more problematic.