I'm a big fan of the remodel cans, but fishin' wire with finished ceilings is going to be where an electrician earns his money.

When I switched to LED's in the basement, I removed the remodel cans and used a canless integrated LED similar to these:

https://www.homedepot.com/p/Halo-HLB-4-in-White-Round-Integrated-LED-Recessed-Light-Direct-Mount-Kit-with-Selectable-CCT-2700K-5000K-No-Can-Needed-HLB4069FS1EMWR/306050711

Prior to installing them, I reinforced the back side of the drywall because I have read that removing the lights can sometimes damage the drywall. I cut squares of thin wood panelling, cut the hole and then cut the square with the hole in half. I glued each half to the back side of the drywall with construction adhesive. Lightly clamped it for a few hours, removed the clamps and installed the lights.

There are some good reasons not to use integrated fixtures but I was OK with the trade-offs.