FWIW, I have twice now had overheating problems that turned out to be a defective "refurbished" radiator. The last time around, the radiator shop reported that it was "fine" several times; until I insisted that they "rod it out". Once they tried to rod it out, they discovered that every tube was coated with what they called "mud" (highly technical term there) until they could not force the rods through! This was a radiator that had been recored in the past and was working fine in my previous TR3A before it got wrecked some years earlier.
The one before that was not blocked at all (they did rod it out) but apparently the fins were not in good thermal contact with the tubes. It was the original style where the tubes are just forced through the fins (rather than soldered) and evidently there was corrosion or dirt inside the joints.
There are lots of aftermarket thermostats that will fit. I use a Robertshaw 330-180, which is a "balanced flow" type. Unfortunately, it seems that they quit selling those and I don't know the application information offhand. Measure the outside diameter of the mounting flange and ask your FLAPS to match that.
Personally, I've never been able to tell the difference with the bypass open or partially blocked. Even fully blocked (with a hole drilled in the thermostat so there is always some circulation) did not help with my overheating issues. Then once I had the bad radiators recored I had no problems leaving the bypass fully open. It's worth noting that even the factory eventually dropped the sleeved thermostats (although the bypass passage was a bit smaller on the later thermostat housings).
I also tried three different flavors of water pump, with no discernible effect. Here's a comparison, where you can see the differences Don is talking about. Note that the aftermarket pump on the right had well over 100,000 miles on it when this photo was taken and was still working fine. I ultimately put it back on the engine, simply because it had worked well for so many years and the others didn't seem to make any difference. Unfortunately it started to leak a few years afterwards, so it has since been replaced with a new pump & pulley from TRF.
More comparison at
https://s258.photobucket.com/user/TR3driver/library/TR3-4 Water Pumps