If you try to run a Jett or a Nelson at an extremely rich setting when new (as rich as you have been doing on that no-name engine), it will come to a squeeking halt... the piston will be jammed at about top dead center, and you will have to apply some serious force to the prop to get it out of there... and it will squeek again while you are doing so...
This is caused by two factors: 1) the excess fuel washes the oil film from between the piston and sleeve, and 2) the engine will be tighter than when run up to temperature.
Also remember that when you are trying to move the jammed piston, the oil film gets pressed out from between the crankpin and conrod bearing...

So you can't do the same test on them...

Now I'm not saying this will automatically damage a rod or something, but seeing an engine coming to such an abrupt stop does not seem right to me. The forces on the moving parts must be extreme... as there is quite a bit of energy stored in a fast rotating crank and prop. If you don't believe me, put your hand into the prop of a running engine...

Jett and Nelson racing engines are so tight when new you can hardly prime them by hand... they will most likely get stuck, unless you have a very strong, fast "flick" in your wrist.
Half of the time you even have to run up your electric starter before you hit the engine with it, to prevent a sticking piston.