I'm just homing in on this one line. I think I've caught all your goals. Sorry, if not. Here's my thought:
Constraints:
* Still needs to work with bounded accuracy
* That means proficiency bonus + something on par with stats
* Try not to keep this as a plug-and-play module instead of rewriting a bunch of other stuff
* Personal preference: Skill points in 3E would be a step backwards. Avoid those. YMMV.
With those in mind, here's some implementation ideas:
* Group skills into a handful of categories: Social (intimidate, persuasion, intuition, deception, etc.), exploration (survival, investigation, animal handling), knowledge (history, religion, nature, medicine), cunning (stealth, sleight of hand, perception), and physical (acrobatics, athletics).
* Each class has "Affinities" for certain categories. Some classes may have "minor Affinities" in a category.
* Rogue might get Affinity with Cunning and Physical, with minor Affinity for Social. (Or pick two of the three for full Affinity and the third is Minor.)
* Rangers might get Affinity with Physical and Exploration, with minor in Cunning
* For single-classed characters, an Affinity essentially adds a bonus equal to the Proficiency bonus. Minor Affinity grants half this value. (Design note: this should be roughly in line with the primary and secondary ability score bonuses, math-wise. At least enough to be balanced and decoupled.)
* For multi-class characters, we treat it a little like multi-classed casters:
* Create an Affinity table that pretty much looks exactly like the Proficiency bonus advancement.
* Classes with Affinity add their levels together to determine the character's Affinity bonus.
* Classes with Minor Affinity add half their level to determine Affinity bonus.
* Classes with no Affinity don't count.
Design note: Why use categories? Because not doing so would be redundant with selecting proficiencies. By grouping them into categories, characters can have an affinity for something in which they're essentially untrained. This allows for greater variation in characters.
Alternate system for avoiding categories:
* All classes grant affinity for all skills listed as options for Proficiency.
* It may be appropriate to refine this list into full and Minor Affinities, potentially expanding the circle of skills.