Kohler Commander CH23 engine into 620

Are you trying to couple the flywheel (non-PTO) side of the engine to the transaxle?  If so, yes, the flywheel side PTO needs to be fitted with an accessory, and there are flywheel PTO adapters made for this, typically they'll be for a specific application, and if you happen upon one of those applications in the recycle ranks, you liberate it.

I put a Vanguard 23, then a GX660 in my Cub Cadet...  I had to make PTO adapters for both.  It wasn't difficult, but I have machine tools at my disposal.

Typically, these engines will have mounting bosses in the flywheel specifically for the PTO accessory.  Sometimes what they'll do, is make the PTO accessory a two-piece item, where ONE replaces the flywheel washer and has a 'drive pin' in the flywheel... remove the flywheel nut and washer, drive in the 'drive pin', then place the 'cup' portion of the adapter onto the shaft, and install the flywheel nut with a socket...  and then the PTO shaft stub flange bolts to the adapter.

Other times, you just remove the screen, bolt the adapter's stub flange directly to the flywheel's preexisting bosses, and then replace the screen.

I have a CH-23 vertical on my  commercial zero-turn, and I'll be popping the shroud and screen off for a little service work here in another week or so... if my CH23 (a Command 7000 series) has same setup as yours, I could whip you up one... just let me know what you want on the shaft size for your mating coupling.

When I get back home (next week) I'll post pix of my Honda's adaption, and pix of my CH's flywheel.  Post yours, we'll compare.  Requires about 2 hours with lathe, mill, drill, and welder, some scrap plate and tubing.

So... I'm NOT an AC garden-tractor guy, I'm mostly Cub Cadet with my stuff, so don't misinterpret my ignorance...

What I'm seeing, looks like a driveshaft to the transaxle, where the FRONT end of the driveshaft is on a swinging arm, springs hold it DOWN, and the drive belts go from that lower 'movable' pulley, up to the two FIXED pulleys on the flywheel side of the crankshaft... and depressing the CLUTCH pedal lifts the driveshaft's front end and sheaves up TOWARDS the engine pulley, which makes that now a 'clutch'?

It appears that the two belts work together (they have same function, they're just a matched pair?

If so, the driveline really only needs to have some doohicky turned that fits onto the flywheel's aux PTO bosses, and accepts a pair of machined steel V-belts... yes?

Take all the adapter stuff you might have in there, and get it out of the way, lemmie see your flywheel with the grass screen, and whatever auxiliary PTO mountpoints may be in there.

I suspect It is probably much easier to make than it seems.