Hit Dice Redux

I'm actually not committed to any change of the hit dice and "to hit" progression tables, but I figured I should provide a better explanation of my previous post. Here's the LBB hit dice progression, as best as I can recall (still haven't located my copies...)

Level  Fighter   Cleric  Magic-User

1      1+1         1        1
2       2     2     1+1
3       3     3      2
4       4    3+1     2+1
5       5     4      3
6       6     5     3+1
7       7     6      4
8       8    6+1     4+1
9       9     7      5
10      10     8     5+1

These are all in d6+adds format. Now, for monsters, you can take the monster hit dice and add that to the result of a d20 roll and adjust for the target's armor; on a 20 or higher, the monster hits. That works for S&W White Box. For Labyrinth Lord, you also have to round up to the next hit die if a monster has bonus hit points, and the formula only works up to 8 hit dice. LBB doesn't match this progression and actually advances quicker, but doesn't progress past 12 HD; if a monster has more hit dice, it's harder to kill, but doesn't get any better at hitting.

What would be cool is if you could simplify the character "to hit" progression by linking it to hit dice as well. The problem is that the "to hit" bonuses go up too fast if you do this. This is what I was mulling over in the previous post.