I would like to try and generate some discussion around this enhancement and how to best use it in any creative build concepts. I am personally not that interested in whether said concepts are admirable performers in EE content but be warned that others may be.
To be clear, TYWA allows use of CON modifier for damage for one of two mutually exclusive sets of weapons: either all axes (includes throwing axes) or all picks/hammers (includes throwing hammers).
Obtaining TYWA is going to cost minimum 18 AP in the dwarf tree. Here's a likely scenario with 2 filler AP used in Dwarven Runes:
Taking the prereq chain gives +4 hit and +4/+5/+6 damage depending on the weapon. The core enhancements give you +2 CON and +30 HP. So consider that all together as part of this 18 AP package.
The obvious build implications I see are:
1. Max CON and find synergies with other CON based enhancements. The benefit to maxing CON using TYWA is that you're maxing both HP and damage with the same stat.
2. Find synergies with a to-hit stat. I'm not aware of any way to use CHA or WIS to hit; are there any axes, picks or hammers that grant CHA/WIS to hit? The only weapon I know using CON to hit is Unkor's Cleaver. That leaves likely candidates STR, DEX, and INT.
3. Dwarven axes are a special case as far as their qualification as two handed weapons when wielded in main hand with shield or rune arm.
Stength to-hit: STR is still required for certain feats like power attack, thf line, overwhelming critical, etc. So there is a limit to how far you can dump it and still pick those feats you want. Your tactical feats will suffer as well. The less you dump STR, the less obvious the benefit of CON to damage becomes. We can be open to finding a combination where STR isn't entirely dumped and we have a viable to-hit from it.
Dexterity-to-hit: Practical options are the Finesse feat, Ranger level 3 or a centered Kensai/Monk mix. These all limit your available weapons to light classed (handaxes, light picks, and light hammers). Ranger Tempest core ability gives DEX to hit with light weapons as well. It's also worth noting that Tempest level 6 core ability Graceful Death gives DEX to damage with light weapons. Monk Ninja Spy core ability gives DEX to hit with piercing and slashing weapons, "when centered". But the next core ability at level 3 also adds DEX to damage with piercing and slashing weapons. So the challenge with those options is identifying a reason to use DEX to hit where it's not already better to go all the way and max DEX for damage too.
Intelligence-to-hit: Granted for axes, picks, hammers only one way that I know, which is with Insightful Strikes artificer spell.
I know the artificer angle has been discussed a little already, and I was scratching together a 15/3/2 artificer/barbarian/rogue to try on Lamannia myself which I'll post up later to get some ball rolling.
Please feel free to add some ideas or build concepts for this enhancement!