Gulliver Jones pre-dated Edgar Rice Burroughs' John Carter novels. He wasn't quite as swashbuckling as Carter though and completely eclipsed. He pops up from time to time such as in the League of Extraordinary Gentlemen and teaming up with Carter over at Dynamite Comics.
None of the Doc Savage stories are public domain. Street & Smith were very good at renewing their copyrights, so don't look for Doc, the Shadow, Justice Inc., falling into public domain for about another decade. But there are plenty of similar pulp characters who have at least their first story if not entire run public domain: Thunder Jim Wade and Jim Anthony if looking for a Doc analogue.
I don't think they're the same guy.
You're right about GullivER. But GullivAR is different.