REGARDING AP:
I feel "AP" should mean a lot of things.
A Dagger is very good for switching through mail junctions or for piercing leather....but it will be wuite useless is thrusted in the middle of a bronze cuirass.
On teh otehr hand I feel that a heavy Axe, just like a Mace, will do damage to a cuirass-wearer by bending the plates with its sheer weight and momentum.
IN ANY CASE, you should be happy that Conan deals with AP in two different ways (Normal & Finesse).
There's not so much space to discuss the rules, but I'll tell you their effects.
But if the AP of rough Axes and Swords beats Armour, the armour is halved.
While if the AP of FINESSE weapons (like daggers) used for finesse beats the armour completely bypass the armour!
REGARDING BIPENNISES:
Another problem is that, archaeologically speaking, as far as I know, we do not have so much evidence for fully functional (not ceremonial) examples of Bipennises/Labrys from the Ancient World...
And even the possibly cerimonial examples are very few and badly preserved...so who knows!
Maybe a one-handed bipennis gots 2 blades, but lighter than a single blade of the corresponding one-handed Axe, so maybe less damage but quicker weapon!
Or maybe 2 light blades = 1 single heavy blade, who knows?
Have a look to the link below and the (possibly) ceremonial small Bipennis.
It does not look that heavy!
http://www.novinite.com/view_news.php?id=129942
Looking for possible 2-handed examples we can check the one figured in this Late 4th-century-BC mosaic from Pella (Macedonia), see the left hunter.
http://en.wikipedia.org/wiki/File

eer_hunt_mosaic_from_Pella.jpg
Even this two-handed bipennis does not seem to have very big blades.
I feel that one thing was the real Bipennis used in antiquity (lighter weapon), the other is the fake Bipennis with large blades from Conan movies and comics.
Maybe, even if I want to keep bipennises for all the three types (Light, one-handed, two-handed), I could make double stats for lighter, realistic (?) versions (less dmg, quick) and heavier fantastic versions (more dmg, slower) = 6 different bipennises!!
The Heavy versions should deal more damage...but with a -1 penalty on Melee!
Maybe the light versions deal as much damage as the equivalent heavier single-blade axe (physique of the blades) and be used for counter-attack at a very minimal level for those with the Martial Proficiency: +1 to Melee.
It remains that real experts will get the most from such weapons: people with the False-Edge Cut feat gets +2 to Melee, and Weapon Focus gives +1 to melee.
So we could have:
LIGHT BIPENNISES:
Small Bipennis (Modified Axe):
1) Light version: dmg 1d8, triple stats: 1/5/1.
2) Heavy version: dmg 1d8 +1, triple stats 1/3/1
ONE-HANDED BIPENNISES
Bipennis (Modified Battleaxe):
3) Light version: dmg 1d10, triple stats: 3/2/2.
4) Heavy version: dmg 1d10 +1, triple stats 3/0/2
TWO-HANDED BIPENNISES
Great Bipennis (Modified Double-handed Axe)
5) Light version: dmg 1d10+1d8, triple stats: 4/1/2.
6) Heavy version: dmg 1d10+1d8 +1, triple stats 4/-1/2