I like all of your ideas but I would like to revise them a little and see what you think. We would see a description of each skill in the Player's Handbook like this.
Keep all the progressions for skills at +3 or -3 so they are easy to remember.
The skill titles would be like this. You earn +1 to a skill every other level-up.
You get an automatic +3 when you are trained, which makes you Proficient. Once you get +6, you earn the title Adept.
Novice +0
Proficient +3
Adept +6
Expert +9
Master +12
In the Dungeon Master's Guide, there will be each skill listed with an Easy DC10, Moderate DC13, Hard, Very Hard, and Formidable description.
Then there will be a 4th Edition Style listing of 3 possible described outcomes.
If you roll -3 or lower and fail, there are negative consequences.
If you roll the target or 1 or 2 more than the target, you succeed.
If you roll +3 or higher and succeed, there are benefits.
There are a few things to address here.
While it is conceptually sound to increase ranks by 3 to match the DC progression, even +6 is a very large bonus within bounded accuracy, let alone a +12.
Personally, I'd like to get away from the granular increases. With ranks that provide a +2 or +3, your choice of skill increase actually feels like a meaningful choice.
Your last idea, though, where there are degrees of success or failure is something I've enjoyed in other games and would make an good module in D&D. I wouldn't do it by default, because it adds complication, but I would probably play with it.
The skill mechanic that I still find the most compelling, though, is the one that provides a minimum d20 result on ability checks. For example:
Untrained +0
Proficient +2, minimum roll of 5
Expert +4, minimum roll of 6
Master +6, minimum roll of 7
Which equates to a minimum total of 7, 10, and 13 respectively, numbers that equate to the Trivial, Easy, and Moderate DCs.