Thanks for your well-reasoned reply, [MENTION=1465]Li Shenron[/MENTION]. I really appreciate it. You have so many points... let me see if I can quickly comment on some of them!
(If I left something out you wanted a reply to, let me know.)
* Skill list doesn't need to be exhaustive, can overlap, not be fixed, blurred: I know. I want to codify this - we don't play D&D like a free-form game. My players like having clear rules that they then spend time to overcome or abuse

No but seriously, they don't like it if the DM is "making up" things since it makes them feel there are no clear rules, and they prefer it if things are made clear beforehand.
Besides, it's a theoretical point. If you run a prewritten module as written, you end up using some skills almost never and Perception becomes a god-stat. Seriously. Just get a passive Perception of 20+ and every ambush and every trap and every secret just appears in front of your eyes.
* What gamers wanted: Gamers also want to play special snowflakes like thin girls with oversized weapons dealing awesome damage with no Strength, all while they have incredible movement and range. Sorry, but not all things gamers want lead to a better game. (Where "better" means a tighter and more balanced game)
Remember Backgrounds are still a thing. Also Racial Skills. I would say that even with my Redux, skills are still way more open than in 3.x
* Your agreement on skill monkey niche: I don't have anything to add. 5E is falling prey to the classic adage "if everyone is special, noone is". The game just needs to be reined in, end of story.
It is not *me* that's using Perception too much. I'm running official modules as instructed.
* Skill tool mess: You have a point. But then again I am not fixing this primarily to make the game more elegant.
Same skill different ability: In practical play you would seldom use ANY ability on a certain skill. I have allowed for the most common cases that occur in practical play (in my campaign), such as being able to use Intimidated both as a Strong and Charismatic PC or NPC. Do note my Redux is generous to Int use of various skills precisely because Int is so underused currently.
* Spot & Listen: I'm afraid that boat has sailed. I did consider it, but in the end the skill list is so short that I can't justify it. Removing everything except sensing monsters will have to do (everything about finding traps and secret doors is now specifically other skills).
* Gather Information: yes, "Investigation" does not work for me, like at all. I have tried to wrap my head around that skill concept and haven't succeeded even now, sixteen levels later. It just mixes things that to me is wholly separate. And it never makes it clear WHEN it is used in place of Perception; especially in written campaigns. So the conclusion is easy: it maps poorly to the in-game actions I am used to playing with, so Investigation is gone. Do note however that Gather Information CAN be used with Int and not just Cha. But it's a "gossip" skill, yes.
* Adding more skills: not a primary concern. Please note Investigation is gone. Animal Handling and Nature too - all bundled into Survival (and in some cases Dungeoneering). Calming down a wild animal is simply weaksauce in a game where a) animals are weak monsters and b) why not just kill it? So is nature - all practical aspects were stolen by Survival, so we never saw any Nature checks.
The PHB lists 18 skills. My Redux lists 21 skills. Not a huge difference. And one of the additions is Craft, which is entirely secondary (several of my players create characters that are good at doing stuff, from goldsmithing to map-drawing, and I want to encourage that by a formal skill). Another is Might, which codifies things fighters have been able to do already back in AD&D. I want to move away from "Strength checks" to a skill, that allows you to use your proficiency on bend bards and lift boulders checks. The idea is also that multiclassed fighters might not be able to do these things as well as characters that start out Fighters: reinforcing the "strong man" archetype of true fighters - Strength-fighters, that is.
I guess the final addition (out of the three) can be said to be Dungeoneering. In a generic game, yes, this would be an quirky exotic skill. But this game featuring lots of dungeons, and even have "Dungeon" as part of its name! I don't care that some people get offended - dungeon knowledge is a core skillset in this game and 4E had it right by explicitly including it.
The important difference is that (Craft aside) my skills are (to me at least) more evenly balanced in how often they see usage. In no small part thanks to Monster Knowledge. And moving "thief spots stuff" out of Perception entirely.