Let me be sure I understand.
Your alternator seized, the fan belt broke[?] the water pump no longer pumped & the engine overheated enough to cause head gasket failure.
So far, so good?

Next, you pulled the head & checked it for flatness, & rectified it if it was found to be outside service limits. Then you reassembled the engine with new parts as necessary, then left out the thermostat & you still have problems.

OK, when you cook the engine, the coolant level drops pretty low in the coolant galleries & the scale & crud deposits that have accumulated in there become detached from the metal surfaces as a result of the lumps shrinking as they dry out in the coolant passages that are now high & dry.
These lumps usually fall to the bottom of the block.

Next, you repair the engine & leave out the thermostat, ensuring that the flow of coolant on the block will be high as you take it for a good old test run. This coolant flow picks up the loose crud & sends it round the system at high speed.
Now this stuff is no good & is better off being elsewhere so the car manufacturer installs a very efficient filtration device that will capture most of the solid lumps of crud in the first pass.
We know it as a radiator & it does a good job, but sacrifices itself in the process.

The fix?
Pull the radiator & have it properly cleaned out or re-cored as necessary. Also, give the engine a really good flushing out, including removal of the block drain plug [if fitted] & dig through the crud that is blocking the hole using a thin screwdriver.
Flush, dig & flush until no more crud flows out.

I fitted a coolant filter that looks like a cheesecloth condom into the top hose fitting & was amazed at how much more crud it captured. I removed at after a month the first time & washed it out, then refitted it, then at longer intervals after that until it started to deteriorate.

ALWAYS refit a serviceable thermostat, summer or winter & as long as the cooling system is in good serviceable condition, it will perform as advertised. I have run my stock 1200 coupe at highway speed for hours in temperatures of 100f [37c] & it actually ran just a smidgen cooler at highway speed than it does at town speeds.

Oh yeah, if the hoses are at all suspect, then just renew the bloody lot, heater hoses too. No point in killing a perfectly good car as a result of penny pinching.