You are just running out of HP. The real remedy is a higher HP tractor.
The work around is low range for mowing up hill or not pushing the HST pedal down so far when climbing the hill. It takes time to learn the limitations of any machine but most will do what you need. Some will just do it faster. Good luck!
I'm not sure what HP the SE / Cab / AC on-off etc., would take away from the 2610, I do know when I had use of a CK2610 for a few weeks waiting for my CK3510SE, it easily handled the finish mower - incline made no difference, couple of things in operation may effect it; I'm assuming you are not using the link pedal, and you are setting throttle at the 540 RPM mark not the 540E mark - I do not know how high the grass was, certainly do not know what the incline was, but the 2610 that I used had no issues with the mower at all, never even considered low range - mid was always more than enough...
Was the tractor fully warmed up? My NX really stumbles when cold. Tractor runs lean. Goes away once at operating temps. This can take 15 minutes some days.There is something wrong. I had my grandson out the other day and pulled him behind the tractor in a plastic toboggan full, RPMs and the engine stumbles. Even letting up on the HST pedal it takes a while to regain the RPMs. There must be something i can do. Any ideas?
Seems like there is definitely a problem with a brand new tractor; (which really should have been caught during 'make ready') why not take it back to the dealer and make a warranty claim? Are there any other 2610's on the dealer's lot? If there are, compare their performance to yours.