Well, since you say it only happens when you activate the electric clutch mechanism for the mower deck--that's where i'd look first. could be a bad bearing, loose wires, bad switch, or something else, in that area that could be causing the problem.
Or maybe, a stick stuck in the works, keeping it from turning! Check underneath the deck, too, for failed spindles, severly bent blade-s, etc. Don't go buying expensive parts unless you check the old ones!

We need to come up with a wiring diagram for this tractor.
What you say ***"as soon as the PTO is turned off, mower runs 100% fine again/Or, when it stumbles and I pull the interlock "black box"*** does not point directly at the interlock module (in my opinion).
You need to check the battery voltage when the engine is running at highest RPM to see if the charging system is working. After starting the engine, run the RPM up to highest setting and check with your volt meter.
If the charging system is OK you should read something near 14 volts or a fraction more than 14 volts.
12.47 volts is not really a satisfactory reading of a battery with the engine not running. It should actually be near 13 volts or higher.
If your system voltage does not rise dramatically when the engine is running, your woes could be due to the current draw of the PTO clutch pulling the system voltage down too low to satisfy the works inside the interlock module.
I presume the interlock module will go to "default shutdown mode" if there is not enough voltage present to satisfy its internal needs.

What exactly does the "interlock module" do? I have a mid 90s Broadmoor and the last time I tried to use it just the other day, the PTO wouldn't engage. I checked out the switch and it was OK. Pulled all the modular plugs apart in the wiring harness, cleaned the contacts which were crudded up with dirt and re-connected them. Finally, with the ignition on, when I engaged the PTO switch I could hear the solenoid engage normally, but I heard a hissing sound and what smelt like burning electronics. Then I noticed smoke coming out of the interlock module, and a putrid smell like a burning selenium rectifier or carbon resistor.

The book says the interlock module is "untestable". I haven't checked on the cost, but I suspect they are expensive, and I'm afraid if I just buy a replacement and stick it in, and the electrical problem is elsewhere, the new one would burn up too.

I took the interlock module off and cut a hole in the case where the plastic had melted and smoke was coming out. All I could see inside was some kind of substrate and the rest of the case was full of what looked like whitish sand. I poured out all the sand, replaced the module, and re-started the tractor. It started up OK (it won't start with the module unplugged from the cable). When I turned on the PTO switch, it engaged normally, and there was no more smoke from the module. The only thing abnormal now is the PTO light gets extra bright for a split second just when I switch the PTO off; I don't remember it doing that before.

Does anyone know exactly what is inside the interlock module and exactly what it's supposed to do in the circuit? The schematic just shows a rectangle with numbers on the pins.

The mower seems to work OK now, but I don't want to burn something else up running it with a defective interlock module.

What are the numbers on the pins?
IF they are-
30, 85, 86, 87 & 87A it's just a Bosch Relay.
Google that and you can find oodles of info on how they work.

I don't have ANY Simplicity schematics.
Possibly if you provide the machine model and serial numbers, there might be a schematic floating around in cyberspace?

Has anyone figured this out, I'm having the same problem where my interlock module seems to be burning and smells like what donk4kyv said. Did replacing that module fix the problem, because I don't want to put a new one in and have it burn out too.