The sad part is you cannot save this shower for later. To repair the issue with more sheetrock is a waste of money now...and a sure recipe for disaster later.
Mold grows on organic material...the paper on the sheetrock. Add to that it stays wet all the time,...it's in the basement.
My advice is to remove all the damaged material you can now, and replace it with the proper materials in the 6 months from now if you do not have the $$.
At least get rid of all the sheetrock in the shower, and hang some plastic if you have to...with duct tape of course.
In the meantime, research what it is you want the room to look like and the materials you will plan on using, we are here to help you along.