pointing out axe isn't necessarily higher DPS. The autoattack is higher dps, against lvl 20 foes at decent ranks of axe mastery, but that's not really the same as simply higher dps. Sword attack skills have more armour ignoring +damage for less adrenaline, they get dslash, and they suffer less from reduced crit chance against higher level enemies.
Also, why do you want to go strength? IMO axes are better suited to weapon>tactics>strength than swords, because you don't need the same kickstart from enraging that really helps dslash out - triple/cyclone do fine - and 6+1 is sufficient for flail to be effective. Which gives you access to soldier's strike and watch yourself!
I would recommend something like the above build anyway, but I'd take a zealous mod and add power attack or solider's strike depending on whether you go str or tactics, instead of exec.
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