I do think more than one re-release window would be a beneficial idea.
A bi-annual re-release, or potentially even a re-release window tied into the summer event in some way, would be a good way to balance it out. That may also encourage more players to return, and more to join under the knowledge that they could stand a better chance in getting a pet they want.
The pets that would be considered NONs are absurdly priced. While it is a players choice to spend/trade that, and Horror's List is one specific user's rating system that is widely accepted, C$2000 (the amount stipulated on the list as the value for 1 NON) works out to around $110 in real life money*. Granted, players can get C$ from trades or selling their own pets or art, but that money has to enter the system somehow, and very much could be offputting to newer or financially disadvantaged players.
In terms of re-releasing store pets, there could be an argument to put them at an extremely low chance in the re-release boxes, but it is a much more complicated issue as people paid real money to obtain them at the time of their release under the belief of exclusivity. The only way that I can think of that would be in the ballpark of 'fair' is to have a paid single purchase re-release box for store pets only, but then that heavily skews the value. It could also be considered exploitative of the player base in some ways to essentially run a paid gatcha model, and potentially law breaking in some territories as it would be a gambling mechanic. It's a much harder area to approach.
There is also a point to be made in regards to the re-release of store pets that there will always be demand for the ones with the original date. We see it with the re-releases already and people only wanting True Dates. Players would continue to want the stores from their original point of origin, and there will always be players who see the re-released stores as illegitimate.
*5 C$380 + 1 C$180 purchase