i know the bad monkey is a tube-screamer type design, though have never tried it myself. seems quite good though, with a 2 band EQ.
some pedals are better for boosting just leads, and some work always on for a nice rhythm sound. it sounds like you might prefer an 'always on' type of pedal.
i actually like the stock sd-1, but it robs your bass - i like this aspect of it ;) but i can see why people don't prefer this, it is a cheap option though.
i also have a tubescreamer, which is perfect for a certain kind of lead sound. though i wouldn't have it on all the time.
agree with twinfan that a clean boost type pedal seems appropriate, especially as you like the basic sound but want more drive. i'm sure his suggestion of the rothwell F1 is a good one. i like to have a bit more control of my EQ when boosting, so use a RC booster or a modded boss EQ for my clean boost.
the problem is if your doing a pure clean boost, you might notice at some stage that hugely overdriving the input stage of your amp has an undesirable effect on some frequencies - like the bass might become muddy, or the highs might get piercing. with a nice EQ control, you can remedy this, and keep boosting more.
if you have a pedal which does a bit of distorting itself, like a distortion or overdrive pedal with a diode clip or whatever, you can spread the drive over an extra gain stage in the pedal, rather than just throwing everything you have at the V1 of your amp. if the pedals well designed, you can get more 'nice' drive - if you see what i mean.