More and more I like removing 'attack stats' - instead of whatever your stat is, treat it as 5 at 1st, 6 at 8th, 7 at 14th, 8 at 21st, 9 at 28th for attack (or any other system that's decently fair of a progression, can divorce it from the stat bumps entirely). Damage is whatever it says now, secondaries whatever it says now, etc.
I had this same idea the other day. The formula I came up with was 4+ 1/7 your level. (1/7 your level is identical to the stat-bump progression is, except at level 7-8, when it is only off by 1.) Also I start with 4 instead of 5, because an 20 at first level is kind of rare, and will be rarer still if you separate attack from ability score. Alternately, you could describe total base attack bonus as 2/3 your level + 4 (+ enhancement and proficiency etc.), so that you don't need to deal with a pseudo-ability score when calculating attack bonus. Keeping the damage based on the normal ability score makes sense and seems balanced with the secondary ability score uses.
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To address the OP's issue, here's an alternate house rule that might work (but which has its own problems):
Defenses use the WORSE of the two ability scores. If your class gives a +2 bonus to a defense, it doesn't anymore; instead, that defense uses the BETTER of the two ability scores.
Another avenue you might explore is allowing other areas to use best-of-two stats, with a different set of pairings. For example, maybe melee basic attacks could be based on Str or Dex, whichever is better, and ranged basic attacks could be based on Dex or Wis (since aiming is like Perception which is a function of Wis?). Hit Points could be based on Con or Cha (since your "strength of personality" keeps you going? I dunno...). You get the idea. Part of the issue with this, is that 4e doesn't have a whole lot of derived traits to apply this method to.
The way I solved the problem at my table is to charge half-price for stats that weren't used by your class. So dumping points into both Int and Dex maybe isn't very useful, but it's not very costly either. (I don't see why you should pay full-price in the point-buy if you're not getting full value. It defeats the purpose of point-buy.)
-- 77IM