You are testing the output (loudness) of each pickup depending on the pickup selected. Your pickups are 10K. (Van Halen range) These high output pickups act as an extra gain control feeding into your pedal so as result when you use your guitar only on 10 or full up you are limiting your “available” amount of clean tones. Fortunately the output is easily adjusted by the Volume control. The complete part of any pedal circuit starts with the amount of output being fed into it.
I would check out some videos on adjusting your guitar volume control, tone controls and pick attack to allow you a much wider pallet of “available” control over your pedals (no mods required). If you are experiencing treble loss there is a simple mod for your guitar called a treble bleed utilizing a cap and resistor so you don’t lose treble.
If you wish to achieve cleaner tones with your gear it is not necessary to change your pickups but it will be necessary to utilize your guitar volume (reducing the Gain of your pickup output). I am not referring to dificult manipulations similar to the swells produced by Jeff Beck but simply adjusting the guitar volume to eight, six or five depending on the desired tone and leaving it there till a change is required to broaden your overall tone.
Here is the first Video I grabbed which hopefully will be a good start:
I would jump ahead to 1:20 as he is very chatty.
I hope that helps.