Check out this site. Vox and Fender tone controls explained, I think all your answers are there. Read the basics and scroll down to the "Tone stack bass".
https://robrobinette.com/How_The_TMB_Tone_Stack_Works.htm
Seems that the bass is cut by C5 and R10-11-13 making a RC high pass filter, being R11 variable, the cutoff freq changes. The resistance will change from 1.5Kohm to 11.6Kohm
http://www.learningaboutelectronics.com/Articles/High-pass-filter-calculator.php#answer1
There are ways to parallel a resistor to a pot to make it smoother.
I see your bass pot is 10K , but the "output" is in parallel with 100 ohm, so one half is always less than 100ohm. You are by-passing C9 with the bass pot.
Imagine you have the pot at 1/2, you have 5K at one side, and less than 100 ohm on the other side (the other 5K in parallel with 100ohm). That's 50:1. With the pot at 10%, you have 1K at one side , and <100 ohm at the other side. that's 10:1, and you said at that level things are OK.
Seeing this, I think a resistor between the wiper and the end connected to C9 will make it smoother. Imagine you have a 5K resistor in parallel with that half of the pot, when the pot is at 50% (5K), you have 2.5K at that half (5K pot, parallel with 5K resistor), and <100 ohm at the other half, that's 25:1, a bit better than the 50:1 ratio without the resistor. A smaller resistor will decrease that ratio. For example, a 2.2K, when parallel to the pot at 50% (5K) will give you 1.52K, that's 15:1 ratio against the 100 ohm resistor. The problem is that the max resistance will be always lower than the resistor value, so it will never reach 10K, so the bass will never be at max.
Doing this will have unpredicted results in the tone control slope. But I'd try a couple of resistors to see if you find a good balance. I think 5K is a good starting point.
Also, reducing C5 should change the range of the control. I'd try less than 1uF (0.68 perhaps). This shouldn't affect the treble, since high freqs should pass that capacitor.