[Varyon]

Considering this is a Technique that is very rarely going to be at unmodified ST for the success roll (untrained, it's at ST-4; fully trained, it's at ST+3), I believe if the intent were for it to use modified ST for the damage roll, this would have been explicitly noted. So, damage is based on the character's normal (Lifting) ST, probably with the Wrestling bonus in play (so high Wrestling both makes it both easier - ST-2 to ST+5 - and more damaging).

A character with extra damage for Wrench (Limb) / Neck Snap has a few options to get there. A custom Technique could increase damage by +1 per -2 (or +1/die per -4), and would "stack" with Wrench (Limb) and Neck Snap. The character could simply have additional Lifting ST (at human levels, every +1 to Lifting ST is +1 to damage). Optionally, you could allow for Lifting ST that is Limited to only work for Wrench (Limb) and Neck Snap; I'd eyeball it as simply being worth [1] per level (making it roughly comparable to the custom Technique, albeit without the Unique Technique [1] buy-in or the additional [1] for the first level for a Hard Technique).