If it's only the handle spinning then it should be easy to find replacements since you have the part numbers. I had homes in Upstate NY and IL and I had them. These are used in most homes at least since the 1980's if your in snow country. I'm not sure about HD or Lowes but the good old hardware stores and or lumber yards with a hardware section will usually have parts to repairs these. I remember seeing them all the time in the stores. If not buy a new one and use it for parts.
If you look at the installation picture, the part the handle screws to is brass, a few inches down there is a fitting and it is then a copper shaft, or at least plated copper. Maybe this fitting is threaded and it loosened up.
They are quit easy to disassemble. Turn off the main water supply. Remove the screw holding the handle and remove the handle. Inspect the handle if it is cracked or broken. Then remove ID # 6, the packing nut. Notice it reads
left hand thread. Loosen and remove the packing nut by turning it clockwise. Then turn the stem as if you're opening it, (may need to put the handle back on the stem or use a pair of pliers, it should come out. Compare it to the picture in the installation pictures. Any parts are missing is where it broke.
Find a hardware store and a good man will know of these and will know how to fix them. If the body of the unit is good and not cracked open as Gary Swart described then it can be repaired without removing it.
If you do have to remove the unit it is not the end of the earth. If you know about where it is in the ceiling cut the opening no larger then an access panel that can be bought. (here is an example,
http://www.homedepot.com/p/Everbilt-6-in-x-9-in-ABS-Wall-Access-Panel-34055/100149906) after the repair just install an access panel and your drywall repairs may be minimal.