Here is my armchair answer:

It's true that in SUSY theories one can often compute many (perhaps even all, in this situation) quantities of interest but these calculations often rest either up a well-defined path integral formulation (which then localizes (pdf) to a sum of finite dimensional integrals thanks to SUSY) or operator-based formulation (as in the superconformal minimal models).

I think that if you have a formulation for quantum field theory like Martin Hairer's that takes the path integral seriously and works for traditional simple theories like scalar $\phi^4$ theory, then what you would want to do is first construct the path integral measure of N = 4 SYM and *then* show it localizes to a finite dimensional calculation.

My guess is that this will be a lot harder than constructing $\phi^4$ theory unless you can leverage SUSY from the beginning, considering it has so many more fields and exists at a critical dimension for the RG.