Variable Capacitor, Similar Approach With a Twist
I had no luck making a varying capacitor with this exact approach but this post was a good starting point. What eventually did work for me was to use the charge based capacitor model. In place of a value like "100pF" put something like "Q=V(Cval)*x" where Cval is a signal name corresponding to the capacitor control value.
Borrowing directly from the LTSpice help file,
"There is a special variable, x, that means the voltage across the device. Therefore, a 100pF constant capacitance can be written as Cnnn n1 n2 Q=100p*x"