How many HP is that new Honda motor? We have a newly opened Northern Tool Company here in Fargo and I see they have Honda OHV 20 HP twins for just over $1000. That is half the cost of a replacement Kohler KT17. The Honda has a V configuration rather than the KT's flat twin. I think the Honda also has hydraulic lifters which is a tremendous step up from the valve design on the KT. Of course...you can also buy a new V twin Kohler Command with the same features as the Honda...but not for $1000 you can't. I haven't spent a thousand dollars fixing the old KT yet, but what I have spent is countless hours overhauling the old motor.
On the carburetors....unless the throttle shaft is worn out...it should be rebuildable. There really isn't much to go wrong with it as I see it. As long as the float is ok, the needles and seats are replaceable. You can replace the throttle shaft, but I am not sure on that one whether there are throttle shaft bushings or not. I have the numbers on it...I can call and see what a replacement carburetor costs. After spending alot of money on the mechanicals, it seems like a waste to have to put up with a mediocre performing engine due to something like a worn out carburetor.
Since I have both the 682 and the new 3000 series Cub (much similiar to the 2500 series)..right along side each other. I can compare the two. The old tractor, in my opinion, is substantially heavier made with one exception. The mower deck on the new Cub is definitely got the edge on the old design. If I could get the old 682 and the new Cub deck married up....that would be a real machine. The new Cub deck is 4 inches wider (54 inches) compared to the old one, but the most obvious difference is the weight of the new deck. I don't know about the decks on the 2500 series, but the 3000 series have an extremely heavy, solid deck with an excellent roller and caster system on it. It is much heavier than the one on the 682 and the decks on either of my JD tractors also. It is so heavy that it is difficult for me to handle the deck after having removed it from the tractor. To move more than a few feet I have to hook a chain on it and pull it with the tractor. Removing it from the tractor is also easier...pull three pins, remove the PTO shaft and slide the deck out. I really don't miss fighting with that drive belt.
One thing I don't like about the 682...you may have come up with a solution for this one. The way my dad's tractor is set up and I think it is original, you have to pull the LH side panel off the tractor to turn on or shut off the fuel at the bottom of the gas tank. It isn't that hard to get the side panel off and on, but it seems like there should have been an easier way. When we first got this tractor, if you filled the gas tank all the way up, it would siphon off into the motor which is definitely not a good situation. I have thought about putting an inline shut off valve up near the top of the motor just before the fuel line enters the fuel pump, but as of yet I have not found such a valve.