Angle Stop Valve Behind Toilet Coming Apart When Trying to Unscrew The Nut Connected To It
You are correct that trying to repair the stop-valve is a bad idea, and should be replaced.
A reason why your condo shut-off valve is spinning is the thread on the stem has being stripped.  That the part that connects the handle to the stem.  When you turn the handle, you will see that the stem is not turning. 
 In my picture, where the Nut is shown,  It could be a nut or screw there to attached the handle to the stem.  You could try and remove the handle to expose more of the stem.  If you can get a clamping plier on the stem, try to and turn slowly clockwise to turn the water off. The stem should be moving in.  This would be a temporary fix to cut the water off.
You will still need a plumber to repair this if the threads are stripped.
If you are able to turn off the water to your condo, then it would be a simple matter of replacing the broken toilet stop-valve with a new valve with the proper fitting, 3/8" outlet, that matches your tee.