I was watching the Princess and the Cobbler version a while back, and I'm convinced that Ed E. Carroll's voice work for the Thief amounts simply to that stupid laugh that's added in when he does that dance during King Nod's speech. (Perhaps some of the other wheezing and coughing that's ADDED into the Calvert version, too, but I'm not sure about that...)
Ed E. Carroll, judging by his IMDB listing, is an American character actor, who mostly did bit parts in TV shows, made-for-TV movies, and low-grade films during the 80s. Since Carroll is American, I highly doubt that he would have done voice work on the Williams version; except for Vincent Price, everybody else in Williams' cast is British and/or generally worked in Britain. However, the Calvert voice cast was indeed comprised of Americans and/or talent that worked primarily in America. Ed E. Carroll seems to fall into that category.
As for who did the original wheezing and gasping, Patrick and I have mulled over the possibility that it might be Richard Williams himself...but don't quote me on that.