Fascinating topic great read! Here are some of my ideas
A few years ago i aquired a Marshall Shredmaster guitar overdrive pedal and the thing is just brilliant! Sounds like it could be exactly what you need. You'll find one on ebay for about £150. I find it works really well with a bass amp because you can EQ more low end in if you need it.
I use an MXR Bass big muff in the effects loop ( ) This allows me to use the dry control on it to really swamp the overdriven frequencies, however they are always there and there is plenty of grit in the sound.
Check out the James LoMenzo hyper drive by Ashdown, It may be the answer to your problems
Lewis