Are all the thermostat components in place, including the spring loaded valve underneath the thermostat? If that valve is missing or not operating properly, water will bypass the powerhead and the engine will overheat. Seems like you have substituted gearcases and most water pump parts only to get the same result.
Test tanks can be our worst enemies sometimes, although you mention the gearcase is buried deep in the tank. Is the tank clean? Maybe leaves/debris in the tank is clogging the water pick up. It is always worth trying the rig in the actual water to make sure this is not a tank issue.
You mention swapping many of the water pump pieces, but not the aluminum impeller housing, perhaps the aluminum housing is grooved/worn. There is a bleed hole in the impeller housing that must be clear also. You mention trying two impellers, I’m assuming at least one is relatively new. Are you using OEM water pump parts or aftermarket? Several members have reported problems with aftermarket impellers.
Have you had the thermostat off? What is the history of this engine, is it new to you? Is the head/block discolored from overheating?
Is this a fresh or salt water engine?
Finally, you mention resealing the gearcase and that you "haven’t got any water in the oil". A leaky gearcase won’t create overheating problems, I’m not sure if that is what you were asking about though. You have swapped gearcase housings, so I am assuming the SS impeller plate is sealing properly to the gearcase housing. Stripped/broken impeller housing screws, or damaged/corroded casting under the SS impeller plate will create and exhaust leaking into the pump causing overheat problems.
Hopefully some of my thoughts/questions will point out a problem that is quickly resolved for you. Feel free to post pictures if that will help clarify questions/issues.

OK, so it sounds like you have tried a used impeller and a new Sierra impeller. Like I say, members have reported problems with aftermarket impellers, so I would certainly try a brand new OEM impeller. You saw the hot thermostat opened when you pulled it, then watched it close as it closed, so that seems OK.
When you talk about the housing/driveshaft seal, are your referring to the seal in the aluminum impeller housing, or the gearcase upper driveshaft seal which is below the SS impeller plate. In a perfect world, no sealer is required anywhere, but we are dealing with a 50 year old engine so I’m sure none of the metal surfaces are "perfect". In any event, a light coating of the OMC/merc gasket sealer around the outer edges of either seal shouldn’t hurt anything, and is a good idea for the driveshaft seal below the SS impeller plate. It is probably a good idea to use the type M/847 sealer sparingly under the SS impeller plate where it mates to the gearcase housing. But yes, it is best to install the aluminum impeller housing "dry" against the SS impeller plate. The key term here is "sparingly". Too much sealer can surely make a mess. Please don’t remove the upper driveshaft seal (under the SS impeller plate) again if you have already replaced it, regardless of using sealer, you will have to destroy that new seal to replace it. Aftermarket seals should have no effect on the water pump job.
You mention that the relief valve and spring is in place under the thermostat, so that seems OK. No obvious signs of overheating (burnt/discolored paint on block), so that says something may have gone wrong while you were doing the water pump job.
The only other thing we/you have mentioned is the little relief hole in the aluminum impeller housing, too much sealer surely could have plugged that up. You would need to remove the two large screws that fasten the water tube receptacle to the aluminum impeller housing in order to check out the little relief hole. There is a hole drilled through the impeller housing, passing through a hole in the gasket, then through a hole into one of the water tube passages. This hole must be clear to keep the water pump from getting air bound.