remember that if you're going tubescreamer (which by the way is a rock staple) it's going to have a big mid hump that's not to everyones tastes. I have a modded 808 which i got for a good price on the bay but those seem to be not so common these days..
The 808 mod refers to modding to original 808 specs but i guess keeping the various controls of the DX
From what you're looking for a would have said the zack wild but i think you'd be happier with a plain old MXR distortion. I hear great things about the Bad monkey, but if you're going to go the tube screamer route i would seriously consider a visual sound route 808.
For what you're looking for i can tell you one pedal that would do it perfectly, but it's a bit pricier than what you want to spend.. A Sobbat DB-1
also, if you're in the uk, check out these guys.
http://www.pedalmods.com/what you do is select the pedal you will sound right after being modded, buy a cheap second hand working boss of the appropriate type off the bay and send it to them to mod. I hear nothing but good things about them.