You do not have to wear the wrist band on your wrist. I usually put it on my key, or if they insist on it being on your body, on my ankle. Trick I learned from a friend that goes often.
A few bars that I think might have been more up your alley, are Vallarta Cora, Mercurio, Los Amigos, Sama, and Frida. All of them have more Mexican Nationals than the other bars you mentioned. Sounds like you enjoy they type of bar I do, and those are the ones I mostly hang out in all week. Even Blue Chairs bar is not too twinky.
Sorry you got sick. That can happen anywhere. I have been lucky down there, eating at street stands, and from the beach vendors, and not been sick yet. Someday it will probably happen though.