I viewed your pictures of the Sears M18 in the engine bay with interest because I made the same install in my 782 about a couple of years ago and ran into the same issues. I didn't have a KT17 to swipe the exhaust elbows from, but the replacement KT17 muffler lined up the same way. I used the tractor for a year and I never had a problem with it, even though it was only "slip fit." I also noticed that the CC M18's included an additional heat shield between the muffler and the PTO absent from the Sears M18.
I used the original Sears PTO with an old MTD deck up until last year when I tried to mount a 44C deck and was advised to switch to a Cub Cadet PTO because of the deck's pulley size: The Sears PTO is nominally 6 inches in diameter (and the MTD deck's drive pulley was 5" dia.), whereas the 44C had a 4.5" drive pulley which was matched to the size of the CC PTO pulley. The "opportunity" (read "problem") presented by the fitting a CC PTO to a Sears motor is that the crankshaft on the PTO side of the Sears motor is 1" in diameter; while the CC PTO is designed for a crankshaft diameter of 1.125".
I didn't notice if you told us how you resolved this issue.
I sourced an adapter for the crankshaft from evil pay, but I discovered that the same part is available from McMaster-Carr for about half the price. I've also read (I think on this forum), that a larger pulley is available for the 44C deck that would bring its diameter out to match the Sears PTO, but I haven't been able to verify the truth to the claim, and the pulley for the deck would cost far more than the crankshaft adapter and might possibly require a differently sized belt for the deck.
I have the engine tin from an 1862, but I haven't tried to put it all together yet. It seems to me that the slant at the front of the "Cyclops" tractors is a bit more acute than the 82 series; and I know for certain that the muffler extension is a bit longer.
Like you, I found a socket for the relay, although I scrounged a part from another tractor and fit my own connectors to it. I find there are subtle differences between connectors from different vendors. The different connectors require different sockets to stay in place well, so buying the pre-wired socket as you did is the better way to go; thanks for sharing.
I also didn't realize that I would need to replace the pulley adapter on the drive side of the Sears engine until someone on another forum pointed out its absence in a picture I posted. I'm sure you know all about the importance of getting the drive shafted lined up and vibration-free.
Keep us posted on your progress, I for one will be keeping a watchful eye on it.
Jeremiah