Insulation, Radiant and Vapor Barriers - help - cold floor above an uninsulated room

I have a freezing cold floor in the back room of our house on the first floor. It used to be a porch and was enclosed. We live in a rowhome and the back room is above a walkout basement "room" - the back wall of this room is separated from the rest of the basement by a thick stone wall, with the rest of the walls being free-standing and exposed on the outside. At some point, someone tried to insulate the walkout room, but its still really cold on cold days (very drafty). It has electrical and the only pipe in it is a pipe to an outside spigot.

I've read about not insulating under a floor above a crawl space, but I don't think this is technically a crawl space - its more an uninsulated room at the back of the basement. I don't mind seperating this area from the rest of the house and don't worry about pipes freezing.

My plan is to place R19 batts in between the joists under the backroom floor, with the paper side up towards the living space, and put blocks of insulation above the sill plate. I was going to cover the insulation with 4 mil mylar, just to keep it from falling down and getting damaged...

Don't use the 4 mil mylar to hold the insulation up, use metal rods that are designed for your application. You can purchase them where you got the insulation.