Necroing this three year old thread because it's an interesting enough question to merit a response.
You probably can't revive pankration in the Olympics as early as the 1890s. It's still too early. But Victorian and Edwardian combat sports WERE trending in the direction of what, in modern terms, we'd call a form of MMA.
Representatives from the major combat sports -- boxing, various styles of wrestling, Japanese jiu-jitsu and judo, and savate, an early French kickboxing style that was quite popular at the time -- were competing pretty regularly in style vs style fights.
Three of the first five heavyweight boxing champions fought what were essentially MMA matches against wrestlers. A fourth one -- Jim Jeffries -- trained with Ernest Roeber, who held the Greco-Roman wrestling championship. Jeffries also might have fought a match with a savate player, but the newspaper report I saw about the incident seemed unreliable.
Wrestling was even further along. A great process of consolidation had begun in the mid-19th century, and had pitted champions of regional styles against one another. The cross-pollination that had followed more or less created modern freestyle wrestling. (Along with Greco-Roman wrestling which, contrary to the brand name, is actually a modern style). Thanks to the interconnectedness of the late 19th and early 20th century world, Japanese and Indian grapplers (Maeda, Tani, Gama) also had the opportunity to compete against their European counterparts under compromise rulesets.
I'm not as familiar with the French savate kickboxers' mixed style matches, but I know that Charlemont had fought at least one high profile (albeit embarrassing, for all parties) match against a former English boxing champion around this time. A couple other savateurs were also fighting boxers and wrestlers.
There was even a "Neo-Pankratium" movement in 1898, which was basically boxing + wrestling and used MMA gloves.
Unfortunately, most of this ended after WWI. The First World War killed most of France's top savate players, and decimated the cohorts that competed in the other combat sports as well. Jack Dempsey, the roaring 20s' boxing champion, was lucky enough not to serve in WWI; Carpentier, who challenged for his title, was a decorated veteran. A lot of other young men had their professional careers in boxing, wrestling, savate, jiujitsu, etc. interrupted by several years of war, shell shock, starvation, and/or death. Add the demise of the interconnected world system of the Long 19th Century, and you've got a bad environment for "pankration" to develop.
Your best shot is to stop WWI. If you do that, the combat sports will continue to consolidate through style vs style matches. The European and American upper classes fawned over Classical stuff during this period, and "pankration" as an Olympic sport would have given a fig-leaf of respectability to what would, essentially, have become a limited form of MMA.
Stop the First World War, add a little luck, and you might be able to get guys in wrestling shoes competing in something that includes old-timey boxing, savate kicks, wrestling, and MAYBE some submissions into the Olympics by the 20s.
Now, if you want the ORIGINAL rules...nope.