Matt: You win the prize for diagnosing two of the major issues with the installation of the MTD deck on my confuguliated 782, but I doubt you need any spare parts.
You are correct in your surmisal that the center pulley wasn't getting enough grip on the belt. You are also correct that the situation was exacerbated by the idler pulley.
I don't know if I could re-create the 46" deck you pictured, but I discovered that the deck as it was originally installed on the donor MTD looked like this:
(Model 13A0771H055, others similar)
I hope you can tell from the exploded view that the deck was actually driven from the LH pulley. To fit it to the Cub Cadet, the previous owner's mechanic moved the double pulley from the LH position to the Center position. This didn't really work very well, as my symptoms demonstrate (cutting only in the center on heavy grass).
The biggest problem I could see was that when the drive pulley was moved to the center, the idler pulley was in the wrong spot. Instead of "gathering the slack" in the belt, the drive pulley was pulling directly against the tensioner. This also meant that any resistance against the blades meant that the belt was pulled off the center drive pulley even more. The net effect was that I had an 18 HP motor getting less than 5 HP to the grass.
To correct the situation, what I did was to move the idler pulley to the other side of the deck using the same mounting bracket.
It isn't perfect, but I can tell you that it works a WHOLE LOT BETTER than before. I cut the grass over the septic tank and didn't lose any blade speed. I was able to get it all in one pass, not three!
The tractor is now less confuguliated than it has ever been, and I consider it to be fully functioning mechanically. When I get the 44 (or 44A, I can't tell the difference) deck fixed, painted, and installed, and figure out why the light circuit wants to flake out once-in-a-while, I will declare the tractor fully un-confuguliated. (I have to say though, Dennis Frisk was right, this tractor was a mess! I have certainly gotten an education getting it all sorted out.)
The tractor it came from looked like this:
This deck has been installed on MTD lawn tractors as long ago as 1988 up to at least 2009. There are references to Cub Cadet on some of the BOMs, so I'm thinking it got installed on some Cub Cadet lawn tractors too, but I can't determine which ones.
Finally, you missed the fact that the belt driving the pulleys is 1/2" and should have been 5/8". This change alone would have probably gone a long way to resolving the issue. But it wouldn't have done anything about the awful "bouncing" the belt was doing while running. It runs very smoothly now. (I'll worry about reversing the rear pins at a later date, they're working where they are now.)
I'm really happy with it, but I can't wait to get the IH deck on it.