One can certainly doff/don their kit underwater, neutrally buoyant with a BC with integrated weight pockets, or with weight belt...or both for that matter.
If you do the exercise properly, there is no issue of "pop up due to buoyancy".
It surprises me that you are pandering this kind of drivel given your profile lists you as an Instructor / Assistant Instructor / Dive Master / Dive Con.
Do some research on diving a balanced rig for starters, but even if one doesn't have a balanced rig, if the BCD with integrated weight pockets is removed from one shoulder and then pulled around the body as it is removed from the other shoulder, the BCD and tank can be held close to the chest, manipulated, cleared a tangle or other issue if need be, then the procedure reversed. If conducted in a calm and coordinated manner, as it should be, then one will maintain control of their buoynacy and not "pop up" as you state.
I have done this. I have witnessed this. This can be done. Go do this. This is the way!
-Z