Is it the external charge port that makes it a PCP? Or are most pumpers just wasteful PCP's that empty their entire reservoirs with each shot, and need a pump on board to make them useable?
The physics of a pumper are as rigidly restrictive of maximum efficiency as are those governing a springer..and considerably tougher, since we lose much of the energy we put in , as heat, and don't get a fuel burn boost. AC operation lets us recover a little bit of that(ambient heat leaks into the reservoir, cooled with each shot)
We also get a higher average pressure at the pellet skirt than a full dump gun at the same charge pressure...that's where most of the efficiency gains come from.
There are some places a little more can be gained..in low lost volume pumps, low friction seals, and clean flow paths. I think a swivel breach pumper, with a valve set up for an S-curve flow path would gain efficiency over the typical stacked tube, 180 degree flow path.
Adding complex pump linkages is the wrong road to go down, IMO. Weight and bulk take away much of the pumpers advantages over other types..the Paradigm, Independence, and older designs like the Dragon don't appeal to me... bulk and weight are the primary reasons. I bet I'm not the only one that feels this way.
Sure, some PCP's weigh in at 8-9 pounds... but you might as well drag around a magnum springer at that point.
There have been schemes for two stage and stacked compression pumps posted here in the past. If those could be implemented without adding much weight or bulk,that might be useful. Ideally,IMO, the "Millennium" pumper would be under seven pounds and no more than 38 inches long.