Hi Matt,
Sorry, I had thought it was just a simple matter of obtaining an SSL/TLS certificate and changing links in the website to HTTPS.
But doing a bit of searching it is obviously a lot more complicated than that!
Seems a lot of current website software needs updating first, so as you say, it may need a different platform.
I'm clueless when it comes to that sort of stuff, hopefully one of the other members will be able to help.