the D+ will also lose bottom end.
I've tried most of the MXR boxes at one time or another - I'm a bit of an mxr whore!. Unfortunately, they all seem to lose the bottom end to one degree or another. The guitar ones that worked the best though were the Distortion 3 and GTOD which only dropped a little of the low end.
Their bass stuff is great. If you can, try the blowtorch. I know it's known to be more of a synthy fuzz, but at lower gains it can do a reasonable OD
On another tack, have you considered the Digitech bad monkey?
sound great and can be found secondhand for not a lot - around £45 new, £30ish used.
It gets a lot of loe around here, and Max at sfx mods them for more bass too