This is probably a stretch, but is there any way that you could host a web-page for a dyna-map render on the server??
Yes.
MineOS is a whole project that touches on many parts: it does wiki documentation, youtube tutorials, has its own distribution and then there’s the main part, the webui interface.
That said, MineOS won’t stop you from running any software or any other configuration that you want: if you wanted to run a voice chat server, or a content delivery network, or a website for dynmap.
How you’ll run a dynmap renderer is a different question, but MineOS Turnkey (what I’m presuming you’re using) won’t stop you from installing dynmap, nor will it get in the way of using a proxy server, e.g., nginx for having the website and the webui both funnel through a program like that (also, things like apache or httpd work).
It’s even possible to have the webui adjusted to additionally host your map (but this is, unquestionably, the least straightforward approach).
These options are all possible, but I cannot say with certainty that I’d know how to explain it or that existing documentation exists here in the wiki or discourse. But 100% doable, with or without MineOS to have your mapping work on your server.