Hey TMH,
I had to read your post twice to make sure that I was reading it right.... Fins? Waving hands? It sounds like something from the 60's... yelling underwater to scare off sharks anyone?
You are exactly right in reference to depriving cells of O2 - this should be a pounding alarm bell in your head when performing the rescue. Just try to do it logically and methodically.
The only factor that I can see could be relevant at some stage of the rescue out of those you have mentioned would be checking the SPG for tank pressure rather than depth. Depth i don't undestand. Pressure however - this is to check if there has been an out of air situation - this will affect adding air to their BC to assist with lift and will also affect how buoyant they are (empty tank = + buoyancy) However, this hardly worth wasting time searching around for their gauges. You'll find out as soon as you test their power inflator on the bottom.
Your highest priority in rescuing an obviously unconscious casualty is getting them to the surface as fast as possibly without hurting yourself. You can do little underwater to help the victim in this case, so the only things you need to worry about are as follows.
1) On approach - look for any movement or bubbles whatsoever, and a quick look around to see if there may be evidence entanglement or any other dangers (marine creatures etc). Careful not to jeopardise your own safety! When you reach the victim, turn them over if necessary and immediately go for an earlobe/pressure point if available - response to painful stimuli is first point of call and, at a long shot, could wake them up. Waving won't.
2) Assess buoyancy quickly. Are you in boardies/thin exposure suit/semi/drysuit? Adjust weight of yourself and victim as quickly as possible, and lock your arm underneath theirs whilst holding onto their tank valve if possible for more stability. There is conjecture about removal of a flooded/partially full mask underwater. Leave it on as it's not doing any harm. You can take it off on the surface. Hold it and their regulator (if applicable) in place, start your ascent and stick to your ascent rate, managing yours and their buoyancy with your left hand. If they become too buoyant to control easily at any stage (drysuits can be problematic here) let them go and maintain your own ascent rate.
3) Start inflating your BC about 3ft/1m from the surface so by the time you hit the waves, at least one of you will be positively buoyant. Establish +ve buoyancy for them, get
their mask off, their reg out, two breaths straight away. Do NOT bother checking for a pulse. Whilst trying to get breaths in (hard as their lungs MAY be full of water), get your ass back to the boat/beach as fast as possible, all the while counting aloud your breaths in every five seconds. Ditch gear only if it will help water speed and they can do without it. If there is a tender/dinghy, get them in it and open the throttle. You can also start CPR in a tender. At the end of a minute cycle you can spend ten seconds moving or repositioning if need be.
From here you can get them onto a solid flat surface and continue or start CPR/admin of AED etc.
That's all in an ideal world. I've been unfortunate enough to drag a body off the bottom before and it's not nice. Hopefully this helps. It's excellent that you are asking these questions and thinking it through. Rescue is always case-by-case. It comes down to your ability to assess/adapt in a pressure situation - something you won't know until you do it. Adrenaline is a beautiful thing!
Let's see what the thesaurus-wielders make of this one.
Good luck TMH, keep your rescue skills slick.