Okay, I'm coming around to blackbrrd's idea as the most promising. So here is my stab at the "rulespeak" and the beginnings of a specialty.
RULES TEXT
When wielding a pair of finesse/light weapons or a dagger and any other weapon you may use an action to attack one creature with both weapons. Designate one weapon as your main weapon and the other as your off-hand weapon for this attack. Roll both attack rolls and the damage for your main weapon normally. The damage for your off-hand weapon does not gain any bonuses or penalties from your ability score, weapon enhancement, spells, abilities, or other effects. Neither does it deal additional damage on a critical hit, though a critical hit still yields a maximum on the damage die roll.
END RULES TEXT
Two-Weapon Fighting Specialist
1st level feat
Dervish
Benefit: When attacking with two weapons you may attack a creature with one weapon, spend any of your remaining movement, and then attack the same or a different creature with the other weapon.
3rd level feat
Skillful Deflection
Benefit: When wielding two weapons or a shield you gain a +1 bonus to AC.
6th level feat
Two-Weapon Supremacy
Requirement: 6th level
Benefit: When attacking a single creature with two weapons you may roll both attack rolls simultaneously. The higher attack roll is used for your main weapon and the lower for your off-hand.
9th level feat
For the Win
Benefit: At the beginning of each game session the DM gives you a cookie.
(Open to suggestions).
This method seems simple to understand and use, balanced, and feels like I'm using two weapons. Since I'm incredibly pleased I'm going to do my best to break it, to see if it can take it.
Racial weapon familiarity alters the weapon's base damage die. So the rule about bonuses may not apply. A race that had familiarity with say, shortswords, would have 2d8s, where as a single race with a heavy weapon familiarity, say axes, would be using 2d6. That is 2 points of average damage difference.
Questions
1)Is this corner case a big enough deal to worry about?
2)Is the problem with two-weapon fighting or racial familiarities?
(Please no cries about the halfling, there are any number of racial concepts that are non-halfing that would make sense for the shortsword, and still create this issue).
3)Is there a way to phrase the rules around this problem without getting too complicated or gamey?
EDIT: This problem is solved by simply changing the d12 heavy weapons to 2d6. Racial weapon familiarity would then increase this number to 2d8. I don't think that really affects balance elsewhere. If nothing else it throws a bone to the greataxe wielding dwarven warrior. We all know that WOTC is run by a conspiracy of high elves as it is.
I'm editting my initial post to link to this version, so we might get a better spread of new ideas and opinions.
Chris, you have been one of the most vocal supporters of a "one attack" system. If this appeared in the next playtest packet, what would your response be?
Thanks all.