2 Reasons your Jazzmaster is screaming with highs.....
The Tone control gives "capacitance" to the circuit, removing some of the highs. The higher value the pot, the less highs removed.That's one reason Jaguars and JAzzmasters are so bright to begin with, the pot values are 1MEG ohm, instead of 500 or 250K Ohm. This allows more of the highs to pass to the amplifier making the tone brighter (more highs and upper midrange).
Would probably be a good idea to use a 500K or 750K Pot with the Jazzmaster to bring back some of the warmth after you remove the tone control as that 1MEG ohm of capacitance is now gone and those extra highs have no place to go.