I'm in the planning stages of building a post and beam, my 2nd one.  The second floor floor joists will be 6x6 hemlock, 4ft on center, and will be exposed to be seen from first floor.

First frame i did 2x6 t&g pine, works great, makes a nice ceiling below, nice floor above.  that is in a ski chalet that is rustic, wood stove etc......great.

But now I am looking to do another frame, and want to have sheetrock for the ceiling instead of the underside of the floor.  Sheetrock will be laid on top of the joists up stairs.  I would like to have radiant in that floor, and here is my idea, let me know if this is possible:

Sheetrock goes down first on top of floor joists on second floor.  then 2x6 dim. lumber will be laid out on top of floor joists (strapping of sorts) with sheetrock sandwiched in between.  Then the flooring will be laid, perpendicular to joists, most likely the 2x6 t&g pine again.  The result will be a cavity between the sheetrock and floor.  Can i lay radiant in there.?  I am assuming I might have to double up the 2x6 strapping to allow for insulation etc for the radiant install.

I know warm boad is probably the easiest and best solution, but I can't afford their prices.

My idea wouldn't have the pex stapled to the floor, but would basically be laying on the insulation (good? bad? alternatives?).  I would have to align/secure pex using a fastner of sorts.  Would put down some foil faced insulation to help radiate upwards.

headroom isn't an issue.

Is this a possibility or just a halfbaked idea?

First the use of drywall as a supporting structural member will not work. 

You will require some type of insulation in the floor to direct the heat to the upstairs.  4 to 1 rule  4 R-Values of insulation for every 1 R-value of floor resistance.  otherwise it will become a  poor radiant ceiling heating system and a marginal second floor system. 

Warmboard is an appropriate solution but lacks the r-value.  Roth Panel System, better solution.  also the radiant without panel will have to have some sort of plate system for it to work as a low energy alternative.  heating without plates will require extreme higher water temperatures. 

Laying the sheetrock down on the joists cuts down on labor.  Maybe its not a good idea from a compression/sandwich point of view.  But I didn't really think of it as being a structural component.  However, with a bunch of pex filled with water I guess there may be some structural concerns for weight reasons.....

The sheetrock approach can be changed/modified.  Thanks for comments