I've taken the floor up and was met with 80mm of rigid insulation panel (Kingspan), so it's a floating floor, no wonder it creaks so much.
A floating floor shouldn’t creak, if done properly with a flat base below the insulation boards.
Is this the ground floor? You mentioned the option of taking down the ceiling instead, which suggests that it is the first floor, but it would be odd to insulate the first floor like this.
The main surprise is that under the kingspan are heating pipes, and the void for them is made by putting 50mm Kingspan on either side of each pipe, putting a slim piece of wood across them, then putting an upper piece of Kingspan on top. Photo attached.
Hot unlagged pipes below the insulation is ridiculous…. and it doesn’t surprise me that it creaks.
I’ve built a floating floor in my hall, which has a lot of pipes. I would put a continuous layer of insulation boards at the bottom, then pipes on top; where there are no pipes, put down a second layer of insulation boards. To avoid expansion/constraction noises, lag the CH pipes with felt. Then fill the rest of the space around the pipes with rockwool or similar. T&G OSB on top. Of course the question is, what is the un-supported (i.e. less-supported) span across the pipes, and what can you get away with before it starts creaking….
But your challenge is what you can do now, starting with what you already have.
2. Are cables in this kind of ceiling likely to be in conduits only? Any issue with adding cabling without adding the conduit
Conduit is not required, but cables under insulation (in conduit or not) need to account for it so they don’t overheat. Probably not a problem for lighting but other circuits will likely need to go up a size.

