Workaround is to find the problematic recipe (the recipe id is mentioned in the debug logs as per above), go to the Beaker web ui for that recipe, click through to the job which contains it, and edit the whiteboard to delete any non-ASCII characters. In this case we replaced the U+3000 with a normal space character and beaker-watchdog was able to proceed as usual.
We should just switch it over to lxml. It looks to be one of the last remaining usages of xmltramp we have left.