[Breezmeister]

The best description I can give is that when cold, I can go fast and climb a hill and the engine does not feel it, but after a minute,going forward from a stop will kill it and engaging the blades also.
Sorry for the long winded post and thanks in advance for reading it.

When you got the engine, was it plug and play or did you have to mess with the wires ?

You did plug the wires back on to the voltage regulator ?

How old is the battery ?

At the battery terminals, do you have 13.6 volts ?

With the engine running at WOT, are you getting 14 + volts ?

The chances of 2 coils going out at the same time are like my chances of winning the Mega Million......
Unless one was already dead, then the other dying.....
Let us know how that works out......

Fuel valve fully open ?

If you are running saddle tanks, there could be trash partially blocking the pickup/valve at the bottom of the tank. The same goes for the valve to switch tanks if you have one.

Hi ho Hi ho............
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[Breezmeister]

Either the coils, or possibly ...

He put a new carb on it.......Even if he did have the plastic connectors on the original carb, it would not kill the engine......Just make it harder to start.
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[Breezmeister]

My tail.

Yea, been there done that when it comes to electrical problems...I have been burned with what I thought was a good battery. At a minimum, I would do a draw down test.......Free at most auto parts store if you don't have the tool.
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[Breezmeister]

Mmmm...Just ordered some pizza ! AND Battlebots will be on at 8pm. Life is good

So, I removed from the circuit both the solenoid and the oil sensor,

Mmmmm...So you ran the engine with no power going to the solenoid ?
Now for the fuel shut off solenoid to work, power retracts the nipple, it allows fuel to flow. With out power, it will not open/retract. So either the nipple was cut off, or the nipple is/was stuck in the retracted position.

Mmmmmm
Were you even getting power to the solenoid in the first place.... But the solenoid is stuck in the retracted position, then when you pull the PTO, the engine/machine does it shake, rattle and roll, the nipple shakes loose and kills the engine.......Mmmmm

So many what ifs and maybes.......Which makes me come back to the battery, did you get it tested ?

And to quote @J.Baker

You need to be more methodical, and stop skipping all over the place.