Hello Markus,
stunnel is a "standard" *nix utility and probably available for your device. You could run it in the same docker container, most likely.
When using a proxy, we've seen good results with both nginx and lighttpd.
The usual pricing of the pro version is geared towards businesses that make streaming one of their main activities, so that doesn't sound like a good fit for you.
We do also have a non-commercial version available of the Pro version, which costs 10 dollars per month (but cannot be used for commercial activities).
That way we can take a look at what would work for you.
Regards,
Jaron