Just got the app downloaded and installed, and I have some updates. I used TunnelBear (a serviceable free VPN that includes Japan as a tunneling option), and while I could "purchase" the app (it's free, but when you initially install, Google Play adds the app to your account), I couldn't download it over the VPN. However, disconnecting the VPN allowed me to install it, once it was on my account.
Short version: Only the initial addition of the "I own this app" entitlement to your JP Google Play account has to happen over the VPN. Then you can install it from whatever network you want.
So I attempted this on my Mac using Charles (as suggested above) and a tutorial from this YouTube video: https://youtu.be/xL70CLXhF9U (Slightly out of date since Charles has been updated, but it was good enough to help me muddle through)
I did get it to work, but with a few notes: 1) This will NOT work on Mojave or later as the older version of iTunes isn’t compatible and will refuse to install 2) You May run into certificate issues with Charles, in which case please review this page on their site: https://www.charlesproxy.com/documentation/using-charles/ssl-certificates/
In the end, I couldn’t get the older version to install without deleting 3.0.2 off my phone entirely (iTunes issues), but still, I did get 3.0.1 on there.
I hadn’t known about the private server project before the servers shut down so unfortunately I’ve now lost any trace of my nesos by doing this, but thought I’d share the results of my test with you all in case there are any other Mac users out there in this boat.