I would love to get my hands on this sled. These are the kinds of projects I enjoyed working on. I'm limited not being able to be hands on, but will give you what help I can. It's a major problem not knowing the history of the sled because I think the key to solving this quickly is there.
Being an electrician, you are already ahead of the game. I'm going to try and find a manual to e-mail you but will give you the basics of snowmobile electrical theory to get you started. I would ignor any previous repairs and treat this as a new problem. Assume that nothing was done or that it was done wrong and you will not overlook anything.
If your battery goes dead, clearly the charging system isn't working. The tach does run directly off of the stator so that is an indication of a failed stator. The needle on the speedo going below zero is an indication of a direct short, probably in the stator.
The stator is A/C voltage. The voltage should be 40-70 VAC from the three yellow wires. Test each wire to another and to ground. (I don't have the specs for your machine, but will try and have them by morning for you.) Look for open or shorted wires. Warm up the motor, then test again. Compare the readings.
At the battery you should have battery voltage at idle and 14.5 volts DC at around mid throttle.
It's normal on sleds for part of the system to be AC and part to be DC. Snowmobiles in general are the most backward wired machines on the planet.
My gut tells me there is a short in the stator or a broken ground on the stator plate. One of the wires coming out of the stator is a ground. Check that. Also check all of the grounds on the machine. The most important is the one from the motor to chasis. Make a new one if you think it's needed. Arctic Cat used to hook 5 ground wires up to the battery. I used to ground those to the motor and run just one large one from the battery to that post. Trying to get a good connection with a handfull of wires just didn't seem like a good plan to me! Let me know what you find from your tests and inspection and I'll work on getting you a wiring diagram and detailed test specifications.