My suggestions may not appeal to you since neither has a knob labeled "clean" or "blend", but I'm currently working with two OD pedals that are great so far.
I never liked the BDDI. Seemed to color and compress to much, didn't find the OD character useful, and the mid scoop was wrong for me. Reminds me a lot of 90s metal tone. Had it for 10 years, tried it in a several live and recording situations, just didn't stick.
I picked-up a Mad Professor Blueberry and have used it at one show so far. It really sounds more like tube amp OD than most others I have tried. The drive can can be dialed low enough that it functions almost as a clean boost, and it has a nice gradual taper to full drive (which can vary nicely by adjusting your bass output volume). I still hear my basses clearly with this thing (i.e. "transparent").
I stopped making clean blend a necessary criteria for pedals. It often seems a bit counterproductive and I don't find that their usual separation sits well with the rest of the band/sound. The drive control and voice of this pedal seems full enough to me that it functions well without needing an additional clean signal. It just rolls-in nicely like a combined drive/blend and still sounds like bass. For me, the nature control is really what makes it useful. I am able to get this thing from a light drive to something so saturated it's almost like a lighter fuzz (with the nature control rolled back). A bit dark, but versatile. I think the youtube vids are a decent example (check the one by Bass Club Chicago and another one with a drum backing track).
Today I received a Barber Gain Changer. If you check-out JohnK's page there is a good sound clip with a P bass.
Compared to the Blueberry this one isn't quite as "transparent", but close. It still has a nice clean boost ability (more than the MPBB).
Much more versatile. This one is a bit brighter than the Blueberry. I think the low gain character of this one sits more in the realm of tubescreamer clone (maybe...I can make it sound almost exactly like my Sparkle Drive, but I don't know much about circuits and diodes like the real pedal nerds).
The controls are great. I haven't spent enough time with it to name all the labels and functions (and haven't used it with a band), but the three-way toggle seems to act a lot like a mid-presence adjustment.
It does a much wider and gradual sweep of saturation from super-light, almost undetectable grit to super-saturated and aggressive. Great low end retention here, also. Though, I think the Blueberry has a slight edge in the lows. I assume the Gain Changer would stick-out a lot more in a band setting. We shall see.
Prymaxe is doing the 20% off sale right now. If you can do a thorough audition within 14 days, then no money lost if it doesn't suit you.
Edit: After tooling around for hours Saturday morning, my earlier descriptions may not be entirely accurate. New thoughts: Barber is a bit warmer and, to me, more pleasant (than the M.P.) at low gain, and the high gain gets pretty aggressive (in the neighborhood of B3K or Aguilar Agro, still warmer I think). I don't get in to this sort of high gain because it kinda veers over to guitar-land a bit much for my taste. The Blueberry at high gain settings is more beefy and useful for me, and still sounds more like tube OD through my Walkabout. Both great! Gonna run both in a show next Saturday--Barber for light grit mostly with palm muted picking, M.P. set higher to fill-in as a much less saturated/compressed option where I would normally use my Hoof fuzz.
