But I wonder if a Jimmy Page - type push-pull volume pot can work for you. Guitar Electronics has this kind of kits (and my guitar tech can order an original kit from Gibson for my LP, which I am planning to do later this year).
Bottom line: talk to a KNOWLEDGABLE guitar tech if a Jimmy Page - type push-pull volume pot can be installed in a Strat.
And please let us all know if you find a fix!