I spent some time trying to do about that. In the end, paying for Mullvad via Tailscale came to look like the only feasible option. But I suppose that if your personal exit node was behind a router that routed traffic through a VPN...
Discussion
Yes I already have that setup. I’m wondering if I could set one of my machines as an exit node, so all my Tailscale traffic goes through it. And have that machine routed through the Mullvad vpn built in?
Given how flexible and configurable Linux is I blindly assume that that's doable (and I once got the impression that it's been done), but I never figured it out, and I don't assume that it's plausible with more mainstream OSes. That said, given that Tailscale kind of gives their service away, and yet doesn't facilitate what you're talking about, i'm left wondering if there are practical, behind the scenes reasons for the challenge of doing so. In a few different scenarios, for a few different reasons, I've tried to set up networking so that different data goes through different connections, and I've never had any luck with it.
I just came up with perhaps the most ridiculous solution, but maybe your exit node could be a VM that's running on a host system that's running a VPN. It's been a while since I've set up a VM but I feel like you can typically either expose it to your network, which you presumably wouldn't want to do, or have its traffic piggyback on top of the host's machine, which kind of seems like what you want?