I don't think all is quite as happy happy joy joy perfect in the Federation as many would imagine. Gene Roddenberry may have deemed it so, but obviously, the writers and producers he hired thought differently.
However, given the parameters you set forth, Horatio...let's entertain another idea:
What if Khan and the Botany Bay were not discovered by Kirk in his time, but were later discovered by Picard's Enterprise? (Or, more ideally and realistically because of its size, the Defiant?...let's run with the Defiant) As we know, things definitely aren't happy happy joy joy perfect in the Federation at that time. You have the Maquis, who are dealing with their strifes with the Federation and Cardassians.
In addition to being a tyrant, Khan also had to somewhat be a politician. In order to amass his armies back in the 90's, he had to win the hearts and minds of those who chose to follow him. If Khan was able to study the political situation of the Alpha Quadrant at that time, learn the plight of the Maquis, and the internal threat they posed to the stability of the Federation's influence in the AQ, he could begin his machinations to win the hearts and minds of the Maquis. He brings the Maquis a prize....The Defiant, after he's captured it, and claims to be one of them (assuming that just about everyone in the Maquis is ignorant of history, and fails to recognize Khan Noonien Singh...again, big assumption, but logic and physics are going out the window for my premise). The Maquis are overjoyed. (There is precedent....Thomas Riker tried to steal the Defiant for the Maquis once before....and failed. Khan with his genetic supermen could succeed...even against the likes of warrior Worf.) Now, the Defiant is in their hands. They even look up to Khan a bit for his success in having captured the prize they tried for before. Khan reveals his Maquis-friendly plans (saying nothing of his overall goals). The goal is simple at first...to run the Cardies out of the worlds that the Feds had ceded to them. Once that's done (and done efficiently under Khan's supervision), Khan convinces the Maquis that the Federation will not stop with this. He fills their heads with ideas that the Federation has ultimately failed them, and now that they've completely uprooted the plans of the Federation at this point, the Feds will hunt them down like dogs. The only choice is to stand and fight. He mentions guerilla tactics that the Maquis had not considered before. The Maquis are still a fairly moral people though, despite their standing apart from the Federation, so he must tread cautiously, keeping their hearts and minds.
He leads them into piracy. After he's amassed and converted enough of a fleet of cargo transporters into combat worthy vessels, he starts his piratical focus onto smaller capital ships. Scouts, destroyers, science vessels, and even smaller cruisers like the Miranda class. Starfleet is desperately trying to hunt down this pirate force which is suborning their ships and impressing their crews. Meanwhile, Khan's Maquis forces, supplemented by his genetic supermen, continue to build up their fleet, slowly but surely.
Ugh...I'd write more but I have to get ready for a gig.