Welcome!
On the contrary, using 250K pots will worsen your problem.
What you're describing is quite common for cheaper pots, what brand are you using? The first thing I would do would be to change them for quality CTS or other top-name pots. They are not that expensive after all!
You could also do a "treble-bleed" mode to retain some treble when rolling off the volume (this concerns the volume pots, of course):
http://www.kinman.com/html/toneWorks...htm#volumePots