First, you are never supposed to be vertical on the surface when snorkeling/freediving...it is a huge waste of energy, and you will not float as you would when flat horizontal...this is what a snorkel is for--to allow flat horizontal on the surface.
Most freedivers are doing much deeper drops..potentially well below 60 feet--for them, the idea of being positive on the surface is an entirely different issue than it is for you and 12 foot deep dives. They need to concern themselves with shallow water blackout, and other issues of depth and duration...You on the other hand, could not experience shallow water blackout, since you could never significantly change the partial pressure of O2 in your blood on dives shallower than 20 feet. For your 12 foot deep dives and shallower, I would use a slightly negative ( 1 pound maybe) weight at the surface, which you would find would not be experienced as sinking, as long as you slowly swim forward --creating a wing effect with your body that prevents sinking...you can get this with a very slow, no exertion effort.....If you have to swim fast for this to happen, you ARE TOO WEIGHTED.
If you were using freedive fins, you'd find the efficiency a huge asset in resting and keeping heart rate down, and you would also find that with freedive fins, if you "wanted" to carry an anchor up from the bottom, it would be easy to do for anyone in semi-decent shape. With cheap snorkeling fins, this could be impossible.