What is the past participle of bullshit?

I read the word "bullshitted" today and it got me thinking about whether or not it's a transitive verb, and what the correct past participle would be.  UK English has the past tense and past participle of shit as shat, but in Americanese it's shit in the past tense/participle as well.  Bullshit as past tense and past participle just doesn't sound good, so Americanese is out.  Bullshat ... doesn't sound good either.  But, as far as I can recall, there are no, or few, English words ending with "t" that have their past tense ending in "ed", so I think this needs to be made a formal exception to the rule, and bullshitted recognised as the correct spelling.

Actually it seems to be - see the Wiktionary entries for bullshitted and bullshit.  However, Google also lists 86000 hits for bullshat, and only 34000 for bullshitted, indicating that the former is more popular.  Quite possibly because the Internet may have more sites written in or influenced by Americanese.