I can't believe that after all the smart people who chimed in here, your all looking at problems other than the guitar.
Somethings not right, it's either a linear pot, a bad connection that fights for a while then gives up, backward polarity on the output jack, or the pot was (is) fried. we all have in our guitars, what OP is supposed to have, and we don't have this problem. Fixing it with pedals is absurd. The guitar should work like all of ours do, nice gradual progressive volume till its 100%
I've had a couple eggnoggs so I can't think straight, but it just don't sound right. ACME pot? acme makes a lot of stuff, I didn't know they made pots, i think i'd start replacing stuff and I'd start with the pot