I have a small section of my house sticking out with 3 sides. Sticks out 3', and is 6' long. The floor under it is always extremely cold so I crawled underneath it and took off the wood covering to see it's not insulated at all. I'd like to fill up any cracks with expanding foam, then add fiberglass insulation, paper side up, and to prevent short circuiting of the joists to the floor cover that with double-faced foil board.

Would the fiberglass batt with the paper up, and the double-faced foil board (polyisocyanurate) be considered two vapor barriers and cause mold/mildew issues?

Thanks!

Yes.

If it were my house, I wouldn't worry about the "short-circuiting" of the joists, and I'd only install the fiberglass, with the vapor retarder UP against the bottom of the subfloor.

And I'd replace the wood soffit with perforated venting vinyl soffit material.

Cold floors aren't just an issue of lack of insulation.

It's also not a thermal bridging issue, so continuous insulation is kinda like using a plaster cast to treat radiation sickness. While thoughtful, and definitely critical for other issues, it won't solve the main problem here.

The dominant heat loss mechanism for cold floors is stack effect. There's a pressure cycle: cold air is drawn to the floor by the hot air leaking out of the room.

That's why simply insulating the underside with a batt insulation doesn't work. If the batt is supported from the bottom, stack effect draws air through to the air space that inevitably forms between the insulation & the floor, flooding the entire joist bay. If installed with the facing @ the top, what prevents stack effect from drawing the cold air right to the floor deck?

This solution therefore has two components:
a) an air-tight insulation that will remain in continuous contact with the floor deck, preventing the cold floor effects of stack effect.
b) a good air sealing treatment for the ceiling above the cantilevered room, to eliminate the stack effect in the first place.