Yeah but the aldgoat horn bow grip is + HQ from main hand, so logic tells me + HQ for other horn parts would be main hand too. I've always done the buffalo sword grip with main hand for that reason, but I've never HQed one.

The thing with your lumber mention is that HQ with main hand is 8/12/12 +1s whereas with offhand you get 4 +1/2/3. So with lumber there's always a + option for HQ1.