Um - answering myself a few hours later - but this may well be a piece of information that proves very useful to people:
There IS an open-source, full function XML parser written entirely in javascript - and it works very well in Web Workers:
XML-JS
Basically, you just need to include tinyxmlsax.js and tinyxmlw3cdom.js in your worker, then follow the doc for using the W3C DOM.
With very little massaging, I got my code to work with both the normal DOMParser (for when running in the foreground) and the xmljs parser.
Obviously its slower - but that really isn't too much of an issue - after all, you're running it in the background!
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