My Reform synagogue held a joke service (with familiar melodies, but silly or parodying lyrics) on the Shabbat following Purim. While a few Shabbat traditions were kept, most were parodied or skipped. Is there halachic precedence for this anywhere?
It's hard to prove a negative, but I've never heard of what you describe, and I'm somewhat familiar with the Reform community. (I see you tagged your question reform-judaism.)
There is a tradition on the day of Purim to do some silly things, usually at the festive meal (held in the home), but also there are purimshpiels in synagogues sometimes -- dramatic, humorous presentations of the Purim story. These might be in addition to services, but they aren't services themselves.
Purim cannot fall on Shabbat in most places (it can in Jerusalem and in certain other old walled cities). By "Shabbat Purim" do you mean a Shabbat near Purim? I've heard of some (usually smaller) liberal congregations moving their Purim festivities to the nearest Shabbat for reasons of logistics (I guess they think they can't get a crowd both on Shabbat and on, say, a Wednesday night), but I've not heard of ones that change the Shabbat service in the ways you describe. I'm not aware of a source that sanctions, let alone encourages, making a farce out of the Amidah or other regular prayers, even on Purim. I suggest asking your rabbi what he bases his interpretation on -- and, if you get a source from him, I hope you'll come back and post an answer here.
Not on Shabbat. ON Purim, maybe, but even so, it should be after the service, not during.