If it was mine before I spent my money I would what to know what is wrong with the Kohler. Also lots of luck to rebuild a engine for 100 dollars because I have no idea what kit that would be.
For $ 100 you would get a genuine Kohler routine maitanance service pack, you know filters, plugs & oil
Hit man suffers from a similar problem to a lot of my customers.
The inability to distinguish between maintanance & repair coupled with a politeness that prevents then taking something back for a warranttee repair.
If it always felt low powered with 27Hp Kohler then good chance it has been running on one cylinder from day one.
Back to Hitman.
Which Honda 660 did you buy ? There are a lot of engines of that size.
The engine will be a lot easier to diagnose in the mower.
Once out all you can do is look & measure and for that you do need a reasonable technical ability, which I fear you do not have, let alone the tools.
The most common cause of smokey engnes is a blown head gasket, this accounts for better then 1/2 of them
Then comes guides and last by a long way is rings.
You confirm the rings by doing a wet & dry compression test each side on a hot engine.
If it passes then You confirm the head gaskets by checking the engine venting, blowing a lot of oil from the breather = trouble
You confirm both sides are running by ;-
1) checking for a spark on each side
2) feeling the exhaust headder pipe each side for similar emperature.
Good luck with a rebuild kit. Rings ofr Kohlers are $ 40 to $ 60 a side & you have 2 sides then $ 20 for each head gasket and $ 15 for the closure plate gasket we are getting near $ 200