My temptation is to take the D&D 3.5 SRD and modify it with an eye towards the math that creates separation between the levels. For instance, maybe BABs don't advance as fast. This would be a lot of work. If there were another game that fit, I'd be open to taking a look.
Tracking.
I would highly recommend OD&D/AD&D, or 3rd Edition, given your background with PF (the less you have to learn of a new system, the sooner you'll be prepared). I completely agree with the idea of scaling things back. I did the same with my game (heavily modified AD&D), where I created a handful of NPC classes, each with a slower attack and saving throw progression.
Something else to consider: if you make the assumption that the PCs are extraordinary
just as they are, and you adjust NPCs to reflect this, you increase the full range of advancement available to your players without sacrificing the "realistic" feel.
For example: the standard range for ability scores is 3-18. Players roll 4d6 (drop the lowest) and arrange to taste. (This might not be your exact method, but I'm assuming it's fairly standard for most versions of the game.) What if we establish a correlation between a person's ability scores and various factors in their life/background? The majority of NPCs in most medieval societies will belong to some sort of laborer or lower class. These persons are less likely than the upper classes to have access to good food, clean water, good living conditions, etc. If we assign stats to this "peasant class" as 2d6, we create a new standard for the majority of the world. Then, even though the player may think, "Man, I've only got a 13 in Constitution," it's still 6 points higher than the average of 7 for, like, 60-70% of the population.
Obviously, the exact breakdown for these stats and NPC social classes and so on, is variable. It can be whatever makes sense for your world. But the principle is: lower the bar for NPCs and leave the PCs where they are, according to the rules, to create the impression that PCs are better than the average NPC. Then apply the same logic to other rules, like classes and class abilities, feats, skills, etc. Low-level PCs will be more powerful than most NPCs; less powerful than most monsters; and still feel like they have room to grow and develop into something more as the game progresses.
I mention all of this because, in my experience, there isn't an RPG in the market that manages to accomplish what you're looking for. (But I could be wrong; wouldn't be the first time.)