I had the same setup and the same problems with VPN (in my case Wireguard) server availability. While looking for a solution I realized I was trying to dealing with an architecture problem with software.

Instead of trying to find a software solution to work around my WG server uptime issues, I moved the Wireguard endpoint to an OpenWRT router. Now if my router is up, my WG endpoint is up and my network is accessible. I’ve been running this configuration for years and it has been 100% accessible.

I’m comfortable with the security of WG - open ports for WG endpoints are invisible to network scanners because they do not respond at all and appear closed unless they are sent the the correct key. Even if an attacker has some way of knowinf a WG peer is listening on a specific port, cracking a 256-bit key would take trillions of years. I was then free to choose a remote access application without worrying about remote attackers gaining access to my servers because of some company’s failed security.

FOSS VNC server apps work OK, but I found them somewhat limited so I added NoMachine as my primary option and run both. It’s a commercial app but it’s free, and is one of the only closed source app I use. It can be run 100% locally (although they have a paid option that uses their servers). It iallows full control over your servers including file transfer and audio.

Doesn’t check all your boxes, but it comes close.