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yeah i would strongly advise using the constrained model in this paper over a larger one, as a larger one will fit the data better but will sometimes assign loopy economic values to the vanna / volga pricing
I implemented it to do risk on options a while back. I found (a) important to weight liquid strikes more heavily to avoid crazy fits (b) can get a good fit with just three params (atm vol, skew, convexity) except for short dated, where more terms were needed to fit the wings.
short dated SPX skew is the bane of my existence. Have to get pretty weird with it to get vols within ~15bps
Looks like a great book!
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