In terms of putting the tank back on, the PADI methodology is the worst possible. Once again is assumes that your on the bottom (or the surface) and it often results in divers having thier wrist tied together behind their back with a tangle of straps. Far better to get your tank out in front of you get squared away (esp, regulator hose between your arms, and slip it up and over.
I like holding the tank above in horizontal diving position, then superman swim up into the arm holes making sure the primary hose is above the right arm as it comes through; works on the bottom, mid-water and on the surface.