If you gradually lower the mowing height, most of the grass will grow back even if it is mowed that short. Some won't grow back, but if you're overseeding, you probably want your lawn to consist of more of the new grass anyway, so that's not such a bad thing.

You wouldn't want to go 'too low' where the blades could interfere with the grass roots. I think when they say 'scalp', they merely are saying cut it as low as it would leave a stubble where air and moisture have an easy time and where seed can make much better contact with the soil.
Any over application of topsoil would also not meet competition from grass blades.

All this though is given when the heat of summer doesn't bake the ground and cause too dry conditions for the good of growing seed.

I have a feeling your lawn mower will stall out if trying to cut below an inch. Even still, you will have to lower your groundspeed unbearably slow to do it. Basically, you just don't want your existing grass to grow fast that it impedes the new growth--a big concern with KBG, but not so much for perennial rye. Good choice on the slit seeding--it'll thin and stress the existing turf a good deal.

If you plan on overseeding with KBG you need to cut the existing turf to the dirt. The 3-4 week germination of the KBG needs all the time it can so it can compete with the existing turf for sun. I have had great results overseeding elite KBG into p-rye.

Thanks everyone. My lawn is mainly a mix of perennial rye and fescue, with a little bit of KBG, so I am overseeding with elite turf type perennial rye (PhD blend).

My idea of scalping is as low as any given mower will go while still able to move across the turf. This depends on the smoothness of the turf, the type of turf, how thick it is, whether it is dead or not, etc.

When I scalped my toasted RUed KBG yard, the only thing keeping the mower from moving was the level of the lawn, so I was on the second to lowest setting. This left close to nothing on top of the thatch layer. When I came to the areas that I had missed with Roundup the first time and were still green/living/thick, I had a real problem at this level. Mower bogged down big time. All depends on the conditions of the turf and what the mower is trying to roll over and trying to knock down.

The long germination time of the new KBG was the reason I went ahead and killed the existing lawn. I didn't want to go to all this effort just to have the old KBG fight off the new elite seed.

Good points. If you killed off your lawn, go ahead and cut as low as possible. If you knock off high spots, good - it just levels the soil. If you still have grass growing, that isn't going to be possible. In that case, just mow it as short as you can. You don't want the blade to be hitting the ground anywhere because it will damage the crowns of the existing grass and possibly kill it.

The purpose of scalping is to expose the new seed to the sun by clipping off the taller grass. With that in mind, do what you have to do.