Installing a box isn't really a problem The retrofit fixtures you make the connection while it's dangling out the hole and then you stuff the whole thing into the hole and it's held in place by the clips.

The tricky part is getting the box out which can be easy or moderately challenging depending on how it is attached to the framing. I've got a cute little cordless gizmo called a Hackzall that is good for cutting nails/screws holding boxes in. Just make sure the cable is out of the way before you start.

Apparently they can't get the current box out of the ceiling without damaging it, and we don't want to have to do any patching.

Get a wafer for that spot. they look like recessed cans but are only about and inch thick and have a juction box you can simply tuck up in the ceiling. They also offer retrofit kits so you can put the same ones where your current cans are so you dont have to remove them and theyll all match.

The 6” wafer gives you enough room to get that j box out too. cut the nail with a sawzall and then open up the drywall enough to fit the wafer.

I'm not sure why they'd have to damage the ceiling to get it out. That ceiling looks flat and white and patching would be trivial even if you did.

What is wrong with patching it? A simple procedure. I had an electrician install wiring for a pendant light too close to a cabinet (the open door would hit the light), and that spot got patched so well you’d never know it happened.

Yes to the wafer light. So thin it will fit right in.

https://www.beeslighting.com/SP-2-30-W?keyword={bkeyword}&creative={bcreative}&gclid=EAIaIQobChMIs5zlpZCU9gIV1Rx9Ch0rIwXKEAQYHCABEgKE4vD_BwE

Those above surface mount leds are the worst. i installed about 100 of them in an apartment building. they just abiut never sit flush and are obnoxious to clip in and remove.

@Susan Murin: "Yes to the wafer light. So thin it will fit right in. https://www.beeslighting.com/SP-2-30-W"

The driver (https://www.beeslighting.com/PSD15-12) for that light is 8-1/4" long, is required to change the voltage from 120 to 12 volts, and would not fit in the existing junction box which the OP doesn't want to mess with.

Yeah, agreed with the abofe comment. dont get those. the RAB ones are great. they come in 4” and 6” and you can change the color temperature on them. the junction box is also small enough to fit in a 4” opening and theyre 120v.

RAB Lighting Surface Mounts ("DISK34", "DISK", "CCT Field Adjustable DISK Surface Mount", "Edge-Lite Surface Mount 5.5")