Thanks for the advice! Very useful! Just a couple of points I missed earlier: (1) The den floor is higher than the garage floor by several (6?) inches, so I think I am OK with code and safety issues (2) I think the slab is in rather good shape - none of the floor tiles that are down now have any humps or cracks in them (3) The baseboard heating pipe enters the den from the little 'riser' that is created from the step-down into the den at a corner. I fear that trying to extend the pipe to raise the baseboard heater would put the pipe coming up from the hardwood floor, not necessarily against a wall - I think that would look rather funky.
You suggested framing the floor to the same height as the dining room floor and accounting for the thicknesses of the tile, and two layers of plywood. Is it not recommended that tile only be installed over concrete or a mortar bed? I was under the impression that tile installed over plywood would create a problem. Perhaps I could use some sort of cement-board over the first layer of 3/4" t&g? I feel comfortable doing the framing, plywood/cementboard, and installing the tile, but I have never done a mortar bed to prep for a tile installation. I was really hoping to avoid bringing in any outside help. If I can figure a way to raise the heater and keep it nice looking, I could probably extend the pipes, sweat the joints, etc. myself as well.
I am also interested in your comments about comfort, or lack of it due to moisture. The floor feels dry, but your point about the existing floor 'insulating' it a little is well taken. Anyway, I obviously need to think this out more! If you have any other advice, or if anyone else is 'listening' and can add something, please let me know.