If you're OK with the startup cost of 2-3 more files for the viewer bootstrap, you could just fetch the XML data from the microcontroller using JS. I assume the xsl stylesheet is already a separate file.
I don't think anyone is attached to the technology of xslt itself, but to the UX it provides.
Your microcontroller only serves the actual xml data, the xslt is served from a different server somewhere else (e.g., the manufacturer's website). You can download the .xml, double-click it, and it'll get the xslt treatment just the same.
In your example, either the microcontroller would have to serve the entire UI to parse and present the data, or you'd have to navigate to the manufacturers website, input the URL of your microcontroller, and it'd have to do a cors fetch to process the data.
Service workers are already predestined to do this kind of resource processing and interception, and it'd provide the same UX.
The service worker would not be associated with any specific origin, but it would still receive the regular lifecycle of events, including a fetch event for every load of an xml document pointing at this specific service worker script.