I probably would of attached, the plywood first, to the floor joists, then the rigid board to the plywood? Make much of a difference? Yes, the builder followed Code by covering the foam board with a thermal barrier.

floorguy...Thanks for the input... The crawl space is vented and even though it looks very dry and does not get wet or damp, there will always be moisture vapors coming up from the ground? laying plastic sheeting will be quite a chore (limited crawl space) but if it's highly recommended then I'll have to reconsider. I've already installed most of the flooring throughout the house and have just opened up a section of the family room to try to fix a few squeaks and thought I should take advantage of maybe insulating if the benefit outweighs the amount of work. Does insulating between the joists really help with the minimizing heat loss? Thanks!

I corrected your URL and put it in the link box below. In that article Joe Lstiburek recommends conditioning the crawl space which would avoid the problems you are concerned about. He says: "Photograph 5: Conditioned Crawlspace - The way all crawlspaces should look. Dry, warm, part of the house, not part of the outside or part of the ground. Insulated on the perimeter not in the floor. Beautiful." Here is a link that might be useful: link

There are several problems I read here. Although it wouldn't hurt to insulate the ceiling under the room, I don't think that is your problem. You mention you did not see a return. It may have one but doesn't sound like it to me since you mention you keep the door to the room closed and the temp. drops drastically. If you are not taking air out of the room, you won't be letting conditioned air in. The size of the room also causes me to suspect there should be 2 supplies and 2 returns (without knowing the size of your existing system). You mention this room is an addition. I suspect the supply, return, heating, cooling systems were designed for the original sq. footage and was not upgraded with the addition. That doesn't mean things can't be done to improve what you have now. For us to really give you much in the way of more precise helpful information, we're really going to need much more information in return. We can steer you in a direction but you will need to have a qualified tech. to come in and do load calculations and make a true assessment of what really needs to be done. Just sitting here reading what you have mentioned, I can only guess (from experience) that you need some rework done. I may be wrong...maybe the original design was to allow for this addition. A Tech doing a site survey can surely better determine that.