250k 500k pots !!!!
Maybe try turning the volume down on your guitar & up on the amp. I also swapped the tone cap for a .05uf wax paper repro from E-Bay ($6), & the whole guitar warmed up.
But seriously the 1 meg pot goes from 1 meg to Zero, so at half setting on a linear taper pot, the value is halved(500k). If you can find no use for the higher range & want a 500k pot, solder a 1meg resistor(cheap) to the two outside tags of your volume pot & bingo, now you have a 500k pot.
The main problem with volume pots is that they don,t maintain the highs when rolled off(I know, stay with me here). A treble retention cap/resitor combo might help maintain a certain linearity through the range. You can the adjust the EQ down on your amp so it doesn,t sound too shrill.
Other things that affect tone:
Pickup Height, Effects pedals(even the good ones suck tone), Leads etc. So when checking your guitars sound it is important to have a good lead & plug the guitar directly into the amp to assess the volumes influence on tone. Iv,e had some pedals that turned to mud & others that actually brightened up when the volume was turned down.