Since the node voltage above Rb is -Vz, would it be safe to do the analysis as if the value were positive and then change the sign at the end? Also when doing the analysis at Rc for node Vo, would I do 1/Rc(Vo-Vz) or would it be 1/Rc(Vo + Vz)?

 

I would have done:
\(
\frac{V_{o}-(-V_{z})}{R_{c}}=\frac{V_{o}+V_{z}}{R_{c}}
[\tex]\)

 

Since the node voltage above Rb is -Vz, would it be safe to do the analysis as if the value were positive and then change the sign at the end? Also when doing the analysis at Rc for node Vo, would I do 1/Rc(Vo-Vz) or would it be 1/Rc(Vo + Vz)?

Don't get sucked into the "pretend it's positive and change the sign at the end" sewer. Just analyze the circuit according to what is given.

As for how to handle Rc for node Vo, that depends on whether you are summing the current leaving the node or entering the node. You don't say and you don't give use enough to even make a reasonable guess.