What "moves" do you guys do? At AA we do moves that are for maintenance only, not live trips. AA took that in 1983. They could have the baggage handlers do all of them but they found it was not worth it. As far as the heads, they still had to man the trips, but after the ETOPs, PS and items were done mechanics went inside and watched TV instead of hooking up a tractor and waiting to push it out. It increased downtime more than it eliminated heads in the big stations but decimated the mechanics in the small stations, it also increased response time for gate calls, but increased down time is not necessarily a good thing, decimation of the small stations is clearly a bad thing. Too much down time makes the guys feel vulnerable.
You are right to fight for the work, but even if you yield on that issue in favor of keeping benefits that retain value such as time off with pay and health benefits, unless doing that work keeps stations staffed with mechanics that otherwise would not be, the impact to mechanic headcount probably will be minimal. In a PEB situation you would likely have a hard time defending keeping mechanics doing Moves but if you give it up you can cite that as a major move towards the company to the PEB. How much of a dollar value did they place on it? If you give that concession for a gain that keeps its value it may be worth it, assuming you already lost that work in smaller stations. We gave it up, but as usual got nothing to show for it.