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I can then generate the system of equations in matrix form using something like SCAM (https://www.swarthmore.edu/NatSci/echeeve1/Ref/mna/MNA6.html) or a system of equations using Sauce (http://www.electronicsauce.com/p/welcome.html).

Assuming solving the matrix equation Ax = b isn't horrifically expensive, would I then solve this system for every sample coming in to my VST? That is, substituting Vin with an input float ranging from -1 to 1?

Is this how people model circuits for their VST's, or are there other methods / optimizations to be had?