Insulating flat/low slope roof

I live in south Florida and have an "addition" to my house that is original to its construction. It was just an addition to the cookie cutter design of the development. It is tied to the main house roof in so it is fully ventilated through the soffit like the rest of house.

The room has an uninsulated low slope roof and the temps in this room are much higher than the rest of the house. The temp of the ceiling inside measures in the mid 90*s with an IR thermometer. The floor plan of the house makes this room the only logical living room and it gets uncomfortably warm.

We are about to paint the soffit and fascia but before I do that, I was thinking about removing the fascia and sliding rigid foam insulation panels in hopes of reducing heat transfer into the room. I would be just sliding the panels in so they rest on top of the ceiling. One panel of foam in there would leave 5" of space above it for airflow.

It may not be the most efficient way to insulate, but I am not in a position to remove the drywall on the inside or insulate the outside of the roof. Is there a reason I should not do this? I don't forsee any moisture build up between the foam and the ceiling. Will the insulation be effective, even in a small way?

I would appreciate any input.

 

An addition that is original? I don't understand that.

 

Very doubtful. The edges won't be tight, won't be sealed, hot air will go right around it. Your best option is what you aren't willing to do at this point... remove drywall, professionally spray foam the joist bays full underneath baffles.

A Florida room. An original part of the roofline (usually a former covered patio) that was later enclosed to be used as livable space.

 

Ok, is that room facing south or west?