Hi Houstonrob,
you should tell your SharePoint admins that the partial shift to HTTPS would leave possibilities for Man-in-the-Middle attacks. Each HTTP request can be intercepted, read in clear text and may also expose a risk to the entire HTTPS-site.
The mentioned GET-to-POST workaround could be easily customized to use a dynamic POST-back URL. But the better solution would be to not use this workarounds at all...
You may try the recomendation of Cody and fix the leftovers within the HTML/CSS/JSON/JS/etc. code. But for SharePoint it would become somewhat complex...
The best approach would be to look again to the SharePoint site. Check if the site has appropiate AAM settings in place and then check if the embedded Workflows/SharePoint Solutions can be somehow changed to support either "" (absolute) or just "/xyz/file.ext" (relative to root)
Note: Let me know if you really want to have a customized version of the GET-to-POST workaround, its a thing of one and a half minute to changs the code to support dynamic URLs. But again, if I where you, I wouldn't use it... ;-)
Cheers, Kai