There are a few sites that will allow you to operate on Yahoo Japan, I utilise Noppin frequently and find it to be a great service. They take a percentage of the listing as a fee and allow you to bid up to 3x your current deposit. Buyee is also another site that offers a similar service, but I am unfamiliar with their fees/overall service capabilities to comment.
The same could be said about Mercari, I do not know much about using it, I only have secondhand feedback of it - but this thread could help enlighten you further on the types of services offered for the Japanese market.
I totally agree with you, the Pop count in no way represents the quantity for a print run. In all my time collecting Gold Stars now (4-5 years) , I’ve rarely encountered Unlimited Eeveelutions. My earlier comment was based off of POP report findings but also first hand experience. Either people are holding onto these cards and not selling them, or the print quantity was so low that they will rarely ever pop up on the market.
I would value the unlimited print run over the 1st in this scenario purely based off of how “easy” the 1st edition print run is to obtain. I’ve only ever has 1 Unl. Vaporeon and have not seen any appear since, they are just too rare and thus valuable to me to find - in this case, I would happily pay more for the Unlimited PSA 10 Vaporeon than the 1st edition.
AT.