I am not a limit player either, but basically in NL, I just give players like this enough rope to hang themselves with.
Trapping works very well against players like this.

1 example

I am dealt :Qh: :Qc: in the BB.

This fool on my left calls, folded around to me. I check

Flop comes :Qd:

/me checks. Maniac pots it. I call.

Turn :

I lead out 2/3 pot, repping the 9. Maniac calls.

River :

I check, maniac pushes, I stack him.

I realize the play pre-flop is dangerous, and wouldnt do that against other types of players, but it's a great way to blindside players like this.
If it matters, Villain had :Ac: