Hmm. After a couple of games {and some ruleset digging}, I think I've figured out what it is that frustrates me so much. Namely, that a lot of tech advances, even the crucial ones, are dependent on acquiring specific aliens. That, in turn, is dependent on the game's own whim - for example, you can't research power armor until you've researched the Cybermite, which only spawns with Anthropods, which in turn may or may not show up in the game at all, depending on how the game decides to roll the dice for active species. While, in theory, this can be circumvented by capturing various medics, those appear far too infrequently to be a practical solution.
So, my suggestion would be to increase the frequency at which medics and engineers spawn in small ships, as those appear to be {intentionally or not?} the vast majority of craft that tend to spawn, replacing some of the navigators, especially as those are generally worthless when it comes to research. Keeping leaders limited to larger ships is still good, as they are guaranteed to spawn there.
Another option, though more labor-intensive, would be to adapt the tech tree to make use of "junk" rank aliens - researching a soldier, or navigator, for example, gives one free hidden prerequisite for one of the techs granted by other ranks. That way, quantity can become a quality, so even though the random chance of getting the kind of captures you want may or may not be on your side, investing into both capturing and researching enough of the ones that are guaranteed to spawn will eventually get you where you need to be.