Get a new router that is programmed to only connect via a VPN and use that for mining?
Yes, any router that has VPS support will work, and the whole network will be running under VPN, or get a proper router like Mikrotik and rent a VPS somewhere close to you and route all your packets encrypted through that VPS, and your ISP will see that you are connecting to a server in (Germany, Norway) but they won't know exactly what you are doing, the process won't be simple, you will need to have some networking background and use a bit of googling, it's a matter of setting up some L2TP / IPSEC tunnel with some encryption like AES256, some of those algos are weak but then keep in mind the stronger the slower, so you want to find a sweet spot.
If you don't feel like going all that, just get a VPS router, many TPlinks come with easy-to-set-up VPN interfaces, and no skills are required, but the downside is, your ISP will know that you are using a VPN, they just won't know what those packets have in them unless they want to spend the money and time to decrypt them, which is unlikely.
I can't tell for Solo mining, but with pool mining, connected to a VPS in a different continent, using both SHA1 and AES256, there is exactly 0 issues, no rejected/stale shares, and everything works exactly the same when the connection to the VPS or not, my VPS is in EU which is probably pretty close to the pool's server so that's some info to keep in mind, I would assume if the VPS was in Japan and the pool server was in the U.S, with all the delay I am adding, that would probably trigger some lost shares along the way.
I have also tested the same router with Nord VPN, with almost the exact same results.
Use a mining proxy like Antproxy, connect your miners to that proxy, and install VPN on the PC, and the problem is solved, of course, the downside is that you will need the PC to run 24/7, the proxy isn't 100% stable (I have yet to find a dead stable mining proxy) so you are going to write some scripts to watch it and restart it in case something goes wrong.