Do not use glue which will make it worse. Adding a small piece of double sided tape won't work as well.
Could you explain why these would not be a good idea? I always like it whens I can gets some learnin' here.
You are welcome to experiment using different glues and tapes and come back in a short while to let us know if they work. My friend used 3m double sided tape but may be not the one designated (3M 300SLE) for this design and the tape came off after a few days use. He then used super glue gel type and it lasted for only a short while. The already deformed (enlarged/loosen) rubber grip came off again.
I then ordered the piece from Canon Canada online store and the problem was solved in less than ten minutes. He sold the camera after a year and the rubber grip was still in excellent shape. BTW, by using glue, you are risking corrosive stuff passing through the openings on the body(underneath the rubber piece) into the electronic components inside creating further problem.
A few discussions in the forum tell the experience. (60D) I have no knowledge about 5D3 problem in this regard though.