This is recollection from memory, but here goes ...
Unfortunately, my set & add-ons are squirreled away, and I can't get to them to check.

The original "Poker Hall of Fame" oversized $5 set was issued in a black tube in a set of 22 (?), all numbered the same.
Is that how many you have in the tube -- 22 ?

Later on they issued 2 additions -- Popwell and Moore -- to the set (total of 24, according to TCR).
The 2 additions were NOT numbered, as I recall.

The listing on ChipGuide shows pics of 23 of them (the Moore chip is not pictured).
While the ChipGuide shows a reverse picture of all 23 with the same serial number, I think the Popwell (and Moore) chips did not have serial numbers. The reverse side of the Popwell chip may have been copied from othere in the set, rather than the actual chip.

Maybe someone can check their Popwell and Moore chips to see if they have serial numbers or not.

Hope that helps ... and that my recollection is accurate.