If you can apply a PGR about a week before seeding that would help out a lot. I would advise investing in a push mower and using that for the first few cuts. Ideally you should wait about 2 weeks before the first mow, but if it gets too tall before that then mow.

Hmmm...what's a "PGR?" Problem is that given my age, the amount of turf to be mowed, and the inclines on various parts of the lot, the push mower is really not an option. I gather that if I use the lawn tractor, I just wait until I can't stand it any more, and then mow? I always have the height at max on the tractor (3 -1/2" or more), so the new grass is not going to be cut for some time, only run over with tractor tires.

Plant Growth Regulator. Basically it slows down grass growth. Trinexapac for example will cut down your mowing by 50+%. Since it suppresses growth in shoot length, the plant puts its energy into growing sideways and downwards, making for deeper roots and a denser lawn. It also darkens the grass significantly. It also helps a lot with drought resistance in the summer because the plant uses less water. It's a great tool that golf courses have been using for many years, and it's penetrating residential market. It's a bit expensive, but it saves a lot of time on mowing.

The problem with using the tractor is that it will tear up the new grass on turns. If that's the only option you have then avoid making sharp turns on the grass and make sure your blades are very sharp.

OK, good advice. I can take care not to make turns, and I'll just stay away from edges, or use the string trimmer if things get out of hand there.

When slice seeding into an existing lawn, you need to cut the existing lawn very low just prior to seeding. Slice seeding into established turf is akin to very aggressive de-thatching. You are going to bring up enormous amounts of plant residue. You'll need to subsequently either rake the "thatch" or bag it (and hope you don't collect the seed).