Sounds like the original pot isn't of very good quality, since it scrubs off volume too quickly from the top. A good "audio-taper" pot should reduce the volume fairly smoothly (to the ear) across its entire range.

Any good quality 500K audio-taper pot with a push/pull switch and standard length shaft should do the job for you. Stewart MacDonald or Allparts would be good sources. I found the Squier '51 wiring diagram HERE, which shows how it needs to be soldered in. They show a 6-connector double-pole/double-throw push/pull switch, which really shouldn't be necessary for a simple coil-cut, but I'd recommend sticking with that type, since it's the "original equipment". Here's a link to the one I recently used on my Dot rewiring project: