Insulating room above garage

Can anyone recommend the best way to insulate a room above a garage?
The garage is unheated with a plaster/cement ceiling.
The room above has carpet & under the carpet a finished floor.

I was thinking I could just adheare HD rigid foam to the ceiling.
The guy at HD said he was doubtful that it would reduce the heat loss being on that side of the cement/plaster ceiling.

I don't want to frame or drywall.

The home owners had a energy audit done and would like to have the job done properly as to recieve the rebate from the govmt.

Spray foam insulation needs to be covered to my knowlege.

Is there a rigid foam that has a high R-value (R-6)
that doesn't need to be covered?

If there are no products that can be exposed can I skim coat the foam with sheetrock to cover it?

Also was looking at Reflectix, that thin aluminum foil insulation - was wondering if that could just be laid under the carpet. Any ideas of R-value?

The job is in Toronto, On.
The garage is attached, the wall is cinder block.

Thanks for any advise.

Greetings rex welcome to the forum.

How much space do you have between the ceiling of the Garage and the floor above it?
Is it enough where you could spray some insulation into that space?

Your limitations about not wanting to Frame and put some Sheetrock on the Garage ceiling is very limiting.
That would be the simplest way to get this done.
I'd pick something a bit better than an R-6 for it though.

Have a good Day !
S.W.