This maybe a dumb question, but what purpose do the chains serve?
I will add this, momentum is your friend, do not and I repeat do not stop on the way up to gaze at the wild flowers and then take off again!!! do it when the dew is off too ;-) nothing worse than spinning out going up and then sliding going down
Do you have other needs for this tractor? I'm not trying to talk you out of getting one, everybody should own at least one tractor. But there are some much cheaper options that will work as well. For example Hasqvarna sells a 4wd front mount mower with rear steering made exactly for steep hills. But it's just a mower so no loader or rear pto. Also with it's lower center of gravity it'll be stabler but not be as useful if you want to pull a cart or something else on rough ground.
I have a buddy that mows a section of his front lawn with a ride on mower. Its so steep it hard to walk down. He groved the lawn tractor tires and added about 150lbs on behind the seat. Its way to steep to side hill mow. This is prob why he rolled the tractor a few weeks ago. Just a bent hood, he was up and mowing again in 5min.
I wouldnt go buying a new tractor to do this. You may really not get any more traction than a lawnmower with chains and weights.