#1
I'm looking for the best pedal for a warm, fuzzy, static-like distortion that has zero bite at all. I play lap steel, mostly older country stuff, but sometimes we branch out and cover other things, like a Beck song or maybe a Ween tune, and I want something that would give a different sound that the absolute clean that my Cube  20XL produces. I'm thinking something without any bite at all so that it would swell smoothly with the volume pedal. Any recommendations would be appreciated. Thanks!
#2
Big Muff on neck pickup with tone rolled off, Blue Box plus a booster to recover from volume drop, or fuzz factory.
#3
Some kind of Big Muff or a pedal based on it would be my first instinct as well. See this thread for a mind blowing array of options.

https://www.ultimate-guitar.com/forum/showthread.php?t=1709810

Some of these are based on Muffs, some aren't. I think most could do what you're seeking.
https://www.blackartstoneworks.com/pedal/black-forest/
http://www.magneticeffects.net/solar-bender/
http://www.magneticeffects.net/new-page/
https://thorpyfx.com/collections/thorpyfx-pedals/products/the-fallout-cloud-fuzz
http://arc-effects.com/crimson-king/
http://arc-effects.com/big-green/
http://arc-effects.com/shepherd/
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