I recently acquired an 8" 3rd Model Single Shot. It is the only one I've ever seen (50+ years). There are four noted on the Club Gun List. The letter notes only that it was a single unit special order.
Another odd duck is a New Model #3 Target (Those made only in 32-44 S&W and 38-44 S&W----per any/all the books.) This one is chambered for "38 WINCHESTER CTG". It too letters as "------appears to have been a special order for one unit------------." There is no record of the caliber in the available factory records.
I have a .44 HE 3rd Model Target (Model of 1926). It is reputed to be one of "less than 50", "less than 100", "less than 200", and 1 of 96. Pick one. The letter is silent on the number produced, also silent on the scarcity/rarity.
All things considered, I suspect the conclusion reached here will be something along the lines of Mr. Redfield's ("JSRIII") particularly astute statement, which I recall as, "We don't know what we don't know." I have yet to hear it put more succinctly.
Ralph Tremaine