I think I must be missing something, because I can't see how sireth is better than the walking stick for a build that takes pulveriser (L6 LD ability).
I'm looking specifically at the juggernaut build (16arti/2pal/2monk WF) here. Adjusted numbers include dance of flowers twist (+1.5w for centred weapons) and the LD abilities (+1w for L6, +0.5w for imp. power attack, +1 crit mult for devastating critical), overwhelming critical, battle engineer, and deadly weapons. Imp crit: bludgeon is assumed (though not necessary for walking stick). Expected crit adjustment is a weighted multiplier based on the crit profile
2.5[d10] + 7, with various effects that add say 25ish damage post-crit. crit profile 15-20x2
6.5[d10] + 9. Crit profile: 19-20 x 4; 15-18 x 2. Expected crit adjustment = 150% (10%*3 + 20%*1)
2[2d6] + 6, with fracturing adding 7 damage to mobs with skeletons. crit profile 19-20x3
6[2d6] + 8. Crit profile 19-20 x 5; 17-18 x 3. Expected crit adjustment = 160% (10%*4 + 10%*2)
Now, first thing to note: with the 2d6 base damage, walking stick is 1.5 damage per w better than sireth. 6.5[d10] = 36. 6[2d6] = 42. Bear in mind that a large number of swings will be cleaves, great cleaves, momentum swings and lay waste each adding +1,+2,+5,+5 w respectively. Critical damage tier 3 adds 6 damage; this equates to around 1 expected extra damage with the walking stick. So sireth is about 12 damage ahead of the walking stick before factoring in strength adjustments, and not including additional w from tactical feats.
Now in theory, you'd need 120 damage adjustment to get the stout walking stick to pull ahead, but i. a lot of your dps is coming from the area tactical feats, when stout walking stick is picking up an extra 7.5 damage per mob per hit (not including its +10% crit adj vs. sireth). So at about a damage modifier of 60ish, the walking stick is better.
The maths above is rough and ready, but the TL;DR version is:
considering that the walking stick can be acquired very quickly, and is fairly similar to sireth damage wise, why would anyone grind for sireth?
The root of the problem here seems to be that pulveriser is broken wrt sireth. If that was fixed, then the expected crit adjustment for both weapons would be 160%, so the sireth would retain its flat damage advantage with scaling strength.