Welcome to the forum Louie.
I agree with your analysis of the problem (i.e. poor seating of the Morse Taper) but not with the method of resolving it. The proper thing to do in my opinion would be to ensure that the Morse taper is properly seated rather than holding on to the chuck whilst drilling. If the taper is properly seated holding the chuck is unnecessary as Doug's photograph of my demo at York yesterday shows. The chuck I was using has a No2 Morse taper in the tailstock quill and a JT33 taper in the body.
I do however also agree with your suggestion of holding the chuck as you back the bit out of the wood to prevent breaking the seating of the taper. That is good practice and a sensible safety measure.
All of this has already been explained in my tutorial here, where I also explain why I believe holding the chuck whilst drilling is unnecessary.
