Based on your description of the Haunt and its shortcomings, you may like the Dirty Haggard Degrade. The blend can be filtered so all the highs are coming from the dirt, which can be tamed with the tone and gain controls. I use it as a bass heavy mild OD. It's bassier than my clean tone.
Negatives: the gate may cutoff earlier than you want as it is at its core a gated fuzz, there's no overall volume control so you may need to tweak your touch just a little to maintain unity, and because I don't share your ears it may just have all the shortcomings of the Haunt and I don't hear it the same way you do. Bonus is Haggard stuff is very affordable.
Negatives: the gate may cutoff earlier than you want as it is at its core a gated fuzz, there's no overall volume control so you may need to tweak your touch just a little to maintain unity, and because I don't share your ears it may just have all the shortcomings of the Haunt and I don't hear it the same way you do. Bonus is Haggard stuff is very affordable.