There are lots of flatheads running around without thermostats that do not overheat.
so, I don't think thermostats will fix it. Slowing the flow down gives the radiator more time to dissipate the heat but at the same time the coolant is in the block longer absorbing more heat. The stories of putting restrictors in flatheads comes from the jalopy and track roadster racing era, at high rpms two water pumps moved so much coolant it could not flow fast enough through the radiator, so it went out the overflow. They put in restrictors and even cutoff every other fin from the water pump impellors to slow the flow down at 5000 rpms. That is go-fast racing stuff and not for street driving. From everything I've read You want as much flow as possible.
If you have an infrared thermometer, check the temp of the engine on both sides. See if one side warms up faster than the other. Check the temp of the radiator tubes to see if any are blocked using the infrared thermometer. Even new radiators can have the tubes blocked with solder. That happened to me once at work. Another new one I installed on a F-600 had the wrong size tubes and overheated. A new water pump had a loose impeller that wasn't turning. New thermostats that won't open. New parts don't mean they are good, and it drives you crazy because you're thinking that can't be the problem, it's a new part. It definitely can be the problem.
If it is a head gasket normally you would have a shiny plug in that cylinder and you don't have one. Normally you would have white smoke coming out the tailpipe. The usual head gasket symptoms are not here but it could still be a head gasket or even a crack,
You can put a house fan in front of the radiator and see if the temp comes down. It could be an airflow problem but driving down the road it should be getting plenty of air and it was still getting hot, so I don't think that's the problem.
If I was back at work, I would think it was a plugged radiator, but you said its flowing fine. With the cap off and the engine running can the coolant fall through the radiator or does it backup out the filler neck. It should be able to handle the flow at idle with the cap removed.
That combustion leak detector above that Pete posted will tell you if you have combustion entering your coolant. Do not take anything apart before you do a lot of investigating.