Mids can be a bless or a curse. They help defining notes but can get nasal. They may help thickening but can drawn your bass into blury mud, too. But the good side is that it's just a matter of Eq center frequency and bandwidth, though.
To my ears, sounds below 200~250Hz can add fatness to the cleaner or thighter bass tone we get below 100H. The real lows around 80Hz and below are muscular and strong, moves lots of air but are more felt in our bodies than heard. So they're essencial but you also have to raise the low mids to make your bass sound big, to add fat to the meat, to add more body around the bones.
The problem is that they can be obstrusive if excessive. 200~400Hz can makes you sound like "cardboard box" and that region also can mess with all other voices in the mix (guitars, keys, toms, snare, vocals). Above, 600~1200Hz can help define notes, but may make you sound too nasal. Good for a "jacoesque" fretless tone, but can be bad if you want a deep fat tone.
60Hz - Bones, Structure
120Hz - Muscles, Thight
200Hz - Fat, Body, Mud
350Hz - Hollow, Flabby
800 Hz - Nasal, Articulation
1200 Hz - Definition, Hearing Fatigue
2500Hz - Clearness, Attack, String noise
When I hear you saying "twangy", it makes me feel that mids really are the problem, but you can't rip off all mids to solve it. My suggestion would be trying a mid cut sweep between 200Hz to 800Hz, you must hear how it interacts with your lows to feel where it exactly need to be. In 200Hz it will probably kill the thickness you need, in 800Hz it'll probably start decreasing note articulation, but somewhere in between you will find the offending frequency you must tame.
I usualy turn down 320Hz with not more than 1 octave bandwidht and bring back any eventual missing lows with a low shelf eq at 100~200Hz (here I sweep too to find the exact point where I get the deepness back).