Right, I've poked about on Gutenberg, and while all of the various versions of Richard II do have the deposition scene, I spotted that many of the versions have at least one typo:
"That bucket down and full of tears am I" is "That bucket down and FUN of tears am I"
(Heh. In context, that's a funny typo. Anyway...)
From a "one typo implies other problems" point of view, that rules out all but two versions:
eText No. 1776
and eText No. 1512
1776 and 1512 have different stage directions. Ordinarily I'd go with 1776, as its stage directions seem to be from the First Folio edition, but 1776 isn't a standard Gutenberg text. It's presented in conjuction with "World Library, Inc., from their Library of the Future and Shakespeare CDROMS" and is "NEITHER SHAREWARE NOR PUBLIC DOMAIN". The blurb specifically encourages sharing, but there's no mention of whether modification is allowed or proscribed