Or 2) I would remove Luck & make the other attributes a background function in the game. The attributes would improve as skills improved, making skills the foundation of character development.
Health/Stamina/Magicka would increase proportionally to the attributes that determine their maximum as per the previous system. This would cut the attribute tweaking by players out altogether.
The player would determine how the character developed by excercising the skills that would shape their character in the desired fashion. The more correlated skills the player spent time improving, the faster the associated attributes would increase.
The only thing the player would assign would be perks. There would be two types of perks. There would be skill tree perks that add new functionality to a players skills, like add weapon attacks & special effects. Then there would be distinctive perks that give the character new abilities that don't fall under the skill tree perks, like Night Person.
Personally, I think you're on to something. I don't know if you are aware of it, but there is a mod for Morrowind called, "Galsiah's Character Development", that does pretty much what you are describing. The skills that you use contribute towards leveling up your attributes, and does so automatically. IIRC, there are no attribute multipliers upon level-up, though it has been a long time since I've played, so I could be mistaken about that. At any rate, it makes the whole leveling process feel much more organic. The only downside to the mod is that leveling is
painfully slow. Before the announcement of Skyrim's leveling system, I had hoped they would use GCD as a model. Perhaps the new system implements something similar -- only even more 'behind the scenes'. At least, that is my hope. I am having a hard time seeing how the new streamlined system is able to address things like 'becoming' stronger / smarter / more agile, etc. otherwise. IMO, GCD / your system would be the best approach towards fixing the attributes / leveling issue.
http://planetelderscrolls.gamespy.com/View.php?view=mods.detail&id=2030, in case you're interested.