I just did it on a 682 so it's fresh in my memory. Here's what I had to do to give you an idea of what's involved. In my case, I tried to keep the 682' as unmolested as possible in case I or someone would want to put an original motor in it some day.
The two repower sites that I inquired with no longer sell just parts without a motor. It's all or nothing, so I had to make just about everything.
The two things I did buy was the engine mount plate from Performance670 and a 1" - 1 1/8" sleeve for the PTO
The engine mount plate (1/4") + the KT17's original engine spacers (1/2") gave the engine the perfect height. I welded the spacers to the plate.
I had to make my own extension/coupling for the driveshaft to connect to the flywheel. Performance670 may've had something that would've worked but they said it would need to be modified so I didn't bother with theirs. I tinker around with aluminum investment casting so it was an opportunity to put that use.
I made an adapter plate to adapt the PTO bolt pattern to the engine's bolt pattern.
I modified the Predators muffler to have a front exit instead of the side exit.
Since the 682 originally had a coil ignition, I wired in a relay to connect the 670's ignition coils to ground when the key is off.
I removed the needle from the carb's fuel cut solenoid and left that disconnected. I wanted to leave the fuel cut solenoid functionality in place, but since the 682's ignition switch cuts the 12v line during cranking, I would've had to do extra wiring with diodes or relays so some such thing that I didn't want to try and work out right now.
I did connect the oil level sensor to the ignition coils so the low-oil ignition cut function should still work.
I used the CC's starter relay and just ran a heavy wire extension from the original starter wire, which is on the left side of the Kohler to the 670 starter, which is on the right side.
I was able to mount the CC's choke cable onto the engine without any major modification. For the throttle, I connected the CC's throttle cable to the 670's with the little barrel/screw connector that came on the 670. I welded a n extra bracket onto the 670's alternator bracket to hold them in place. It's a little extra complication but again, I wanted to modify the 682 as little as possible.
I think that is about it for the major hurdles. The one oil line to the cooler rubs a little on the side cover when it's in place so I would be concerned with it wearing through after many many hours of use. I think by shifting the oil cooler position a little I can alleviate that.
Impressions?
It runs nice and smooth and is quite a bit quieter than the CC's I have with the M18.
Power? It's got good power, but the CC's I use with the M18 don't seem to struggle with much either so I don't know how noticeable the extra HP will be in practical use.
The charging system, as is known, is weak. With the PTO on, it seems to hold its own when it's at or near full throttle (according to the ammeter) But I'll know better after some mowing sessions whether or not it's going to be able to maintain the battery charge. With the headlights on, the ammeter reads discharge

Of all the obstacles, this is the most annoying as there are no simple fixes.
I've read a couple different options: belt-driven alternator (it'd be quite hard to make that fit I think), 6-magnet flywheel from a Honda (timing keyway is in a different place so would have to be modified), or the most intriguing solution, rewind the charging coils with more windings to increase their output.