I am going to double post for a change, but maybe it will help with problem solving. The tendency is for a person to feel a problem is more complex than it is, sort of like not seeing the forest for the trees.
Overthinking a problem can be misleading, and we all have that fault. I have seen equipment cause very expensive problems which generally turned out to require a very simple solution. A two stroke engine is a simple device, but it is unreal how many good mechanics will balk before working on one. One of the first things people do when they run into a problem is to go through what I call "what if" thinking and complicate the issue.
Here we have an engine which is running and then locks up. Yep, something probably broke or seized, so you want to go over it with the most common problems investigated first. A locked up power head and probably heated parts is the first thing to check. Gear box problems which lock up a motor are seldom encountered and should make their presence known before actually failing. by being hard to engage with possible vibration.
In this case we have a motor of an older design which does not have a lot of mechanisms bolted on. After going through a cooling cycle, it was possible to break it free and turn the engine over. Any internal damage which occurred is impossible to determine without tearing it down, but lack of lubrication should be the first item investigated. It was designed long before TCW and other lubricants were invented. There is a good possibility that this motor will require rebuilding, but sometimes the damage is minimal enough that it will wear back in if parts were not broken when it froze up. If the aluminum piston skirts expanded and galled, they may wear back in. If the cylinder walls were scored or rings broken, it is rebuild time.