Lighting – Should I use remodel or new construction recessed fixtures when installing a new ceiling

We have a stomped ceiling on the first floor in our new home (built in 1969) that we want to get rid of. Every contractor we've talked to says that scraping it off isn't an option because it's been painted over, so we are opting to install another layer of drywall over the existing textured ceiling. We could also rip down the ceiling, but that seems like more work than we want to do right now, but if that's the ideal scenario, please comment on that.

Since I have the opportunity, I want to install recessed lighting because I can cut into the current ceiling and run electrical and cut as many holes as I need to in the drywall since the ceiling will be covered over.

My question is: Would it be better / easier to use remodel or new construction fixtures?

Here are the scenarios I am currently envisioning as options.

1. Install remodel cans into the existing ceiling and then drywall over this with the new ceiling and cut holes for the cans in the new 1/2 inch drywall. This would mean that the lip of the remodel can is stuck between the new and old drywall and the trim that I attach to the can would have 1/2 of drywall between it and the actual can. This is what I'm leaning toward, for ease of installation, but is it a problem to have the trim 1/2 in away from the can, with the trim against the drywall?

2. Cut bigger holes in the old drywall and use new construction cans. This seems like it'd be more work, but I could lower the edge of the can down to the edge bottom edge of the new drywall, so the trim is right up against the can.

3. Install remodel cans into the old drywall and wire them up, then take them down when the new drywall goes up and then cut new holes in the same places and re-install them so the lip is flush to the new drywall (but I would have to modify the clips so they can accommodate 1" thick drywall).

4. Bring down the old ceiling completely and use new construction cans. (seems like a lot of work)

The only other concern I have is that 1-2 rooms are additions to the house where there is no attic access, but I believe (hope!) there is insulation above them. Do either the remodel or new construction install lend themselves to making sure that I get adequate insulation above the cans if I can only access them from below? I am using IC rated cans even when there's no insulation.

Thanks for your input and advice!

EDIT: I did remove the ceilings and it was a good thing too, found several issues including HVAC vents cut off without being replaced so that a few rooms didn't have heat or cooling!