When I was at college, I used a free tier AWS box to allow me to make things inside the school network public through some SSH and proxy shenanigans, and I used the box to let me escape the anti-vpn firewall rules they had by tunneling my VPN service through SSH

Unfortunately, this is a third party, but considering its a cloud platform, it might be a bit more reliable than a third party service.

What bottlenecks are you experiencing on which services exactly?

Not sure what you mean by third party services

do you mean relying on a third party full stop, or do you mean relying on some product(s) only offered by one company?

I have a free-tier VPS, set up a WireGuard server, and port forward over that. Works great, a little bandwidth hit (VPS connection "only" ~400Mbps and my raspberry pi can get CPU-bound on a gigabit over WireGuard anyway).

While this relies on a third party in a general sense, it doesn't specifically rely on any one third party: if I want I can just spin up a VPS on a different provider, change my DNS entry, and I should be up and running.

While something like TailScale probably would work for me and possibly be more convenient, I like relying on just the basics.