Here is what Richard Skeuse replied to me regarding that question based on a label found in the case of my repro:

Hi Don. I have no idea where that label came from, however as I said previously I’m not sure how many P numbered Parker Reproductions were made. I can assure you that there were not 4-5. Numbers started at P 001 I assume but that information was lost in hurricane Floyd. You have the 420th or so that was made. That is all I can tell you about the gun. Thanks
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I believe all of the P guns are 20 gauges and that there are 500 of them.

One can read what Richard Skeuse had to say regarding the P-guns in posts #5 & #7 in this thread: https://parkerguns.org/forums/showthread.php?t=3468

The label is a reproduction of a British charge label that John Bugden filled out for his Repro. It has nothing to do with Repro production. John Bugden is a skilled craftsman and also a gun dealer.

Thank you Mr. Mills. That label in the case would have been great if from the Parker folks, still a nice bit of "case candy". Still a bit of mystery as to how many "P" guns were manufactured isn't there? What have we seen so far as the highest serial number of the original 20 gauge "P" (prototype) guns? Somewhere a little over 400 I believe. Do you, or anyone else, know if all the Parker "P" guns had the Parker Reproduction labels in the top of the case? I have a case that is sans the label.

So the label in Mr. Mills case states the gun was manufactured in 1982. Another bit of information that corrects what I thought. I was under the assumption that production of the guns started in 1985 and ended in 1989. Corrections appreciated.

Frame size and barrel stampings
 

I have owned six DHE 410/28 sets, still own 2 sets. They are OO frame 28ga guns with 28ga barrels marked OO, the 410-barrel sets are stamped OOOO. Two of the sets I have owned, the 410 barrels had the same SN stamped on them as the 28-gauge frame, the other 410 sets did not have a SN on the barrels and were most likely added at the very end of production to existing 28-gauge guns. Also, none of my 410-barrel sets had a SN stamped into the for-end Irion. If the factory would not have suddenly closed, I think this would not have happened. I think the factory miss marked these 410/28 combo barrels due in part to the mini 410 stand-alone gun that was to be a true OOOO frame. There is just not enough info on that subject, and I have never laid eyes on a OOOO frame. I think the 410-barrel sets should only have OO stamped on them and there would be no confusion about the frame size. SXS Ohio

I have often been curious about the scarcity of various configureations of each gage such as pistol grip versus straight stock,double vs single trigger, bevertail vs splinter forearm etc. which combination would be the rarest?

In my opinion and this is only my opinion -- not backed by any documentation of any kind is that pistol grip, beavertail forend with double triggers is the scarcest of all the available configurations offered. This PG, BT and DT configuration wasn't very popular back in the day and remains so today. I'm quite sure many will disagree.

Having said the above, the scarcest of the scarce and so rare that it's doubtful even one exists is a 12ga. DHE w/28" bbls. factory choked Q1/Q2 in any configuration. Another rare bird is the Sporting Clays Classic, offered as a 12ga. DHE with only ~ 125 ever made. You might find them occasionally offered, but those SCCs made with a straight grip, splinter forend and double triggers are exceedingly hard to find.

After more than a year without a post, we are still waiting for owners of 0000 frame, to come forward with serial numbers. I mean real 0000 frames not 00 frame guns with 0000 markings. The assumption is that they are mostly BHE grade guns.

I've posted this pic of a real and authentic 0000-frame Parker Reproduction BHE several times bearing serial number B 410-0052.