Dedicating something like a Raspberry Pi or a Nano Pi to an Amiga is an excellent idea. If you don't have an ethernet for your Amiga, it can do SLIP or PPP over serial and connect to the Internet via wireless or ethernet.
Running stunnel on the Pi is the best way to deal with SSL / TLS. The worst possible way is to turn it all off. With an up to date version of stunnel, you won't have all the SSL / TLS issues that older software has.
There are other things a Pi can do, too, such as act as a web rendering proxy, a fileserver, and more.
