I'm tempted to run AA in a new way, keeping the players more involved and keep the numbers low. One example would be to do the "Getting Rid of the Spread Option."

Another way would be to have players roll a "Damage Save" instead of having the GM roll a monster's attack roll.

The Damage save would be Dex+AC bonuses. The difficulty would be 9+HD of the monster. If you have a house rule for critical hits, the monster gets them on a "1" instead of a 20.

For newbies, the AC looks like a "defensive" version of BTH roll. In reality, it's just flopping the numbers around. I might consider also letting player use a Fate point to do some sort of "Critical Fumble" effect on these rolls.

Any other suggestions?

Sounds like an interesting idea. I'd be curious to hear how it works in actual play. Although, to keep things standardized, if I were to do something like this the base difficulty would be 15 + monster HD (standard SIEGE check difficulty), with the check being a standard Dex SIEGE check, adding AC bonus. This would mean that characters with Dex as a Prime take damage less often, though, which would make Dex something of an uberstat...

This is one of my favorite house rules from the D20 era. It keeps the players engaged, turning AC into a defensive action. The way I run it, the monster (or NPC attacker) essentially takes 10 on his attack and adds Attack bonus (usually just HD). The defense bonus is simply AC-10.

As The Grey Elf alluded to, it would be interesting to see Siege Check version of combat too, but probably not worth the effort to replace the balance of AC and BtH system-wide.

It occurs to me that you could feasibly allow the check to be made by pretty much any one of the PC's ability scores--there's rationale for using just about any one to escape damage...that would fix the balance again.

Strength would represent your ability to physically deflect the blow.
Dexterity, obviously, is the ability to dodge it.
Constitution is the power to absorb the damage without harm
Intelligence is an observational ability to predict your opponent's actions based on their combat style and patterns
Wisdom is an intuitive ability to sense the incoming attack
Charisma is your ability to distract the opponent so his attacks aren't as accurate.

I was thinking on similar lines but with only phyiscal attributes
STR -> Parry
DEX -> Dodge
CON -> Block with shield