Finding the input impedance of this gyrator
I figured out the question, in case anyone else comes across this in the future. Looking in, the negative impedance devices end up changing the value of the resistors to negative, so every element in the circuit except for the R element in pointing downwards is negative. They themselves are not to be counted as distinct elements, rather changing the value of other elements accordingly.

This can then be solved with simple algebra:

$$\frac{1}{\frac{1}{R}-\frac{1}{R+Z}}-R = \frac{R^2}{Z}$$