So just thinking out loud, and this might not be best source for fact based experiences, but I had an idea.

With a track based car, no rules to follow other then common sense/safety/cost/weight, I was thinking for a Florida car, with an old fart driver, with an alum Kirkey containment seat, and less then 30 min track stints, could I just drum up some seat back Ice pack slots attached to the seat back, figure out a basic ambient air insulation solution, incorporate an easy melted ice pack swap between stints design, and be done with it?

Sure it won't be slick or controllable, and will add some weight, but its simple?, reliable, and less then the multi thousand dollar powered systems, and be better then nothing, and its hot In Florida in a 3.5 race suit, in an enclosed non AC car

possibly use a medical ice pack vest under your suit ?
as i suffer from MS, the heat kills me. [but i love the summer !] i use one of those vests often, and always at carlisle.
they are cheap, and so are additional ice packs.
look up cooling vests or medical cooling vests. lots of choices.
the only thing i don't know is how tight your suit fits. these things are not big, but figure the ice packs at about 1" thick or so.

I use a DIY race chiller system from a company called ultra chiller.

https://www.facebook.com/UltraChiller

I've used it on 115'F days in my lemons car at Thunderhill for stints up to 90 minutes and been cool and comfortable the entire time. The systems uses a marine type bilge pump in a cooler full of ice water to pump ice water through a t-shirt with tubing sewn into it. The tubing/shirt goes under your race suit. With the system on its more comfortable in the car than out of it!

-Jon