Is this idea workable?
 

Many years ago, before they became toys of the rich, I owned a (genuine!) 427 Cobra. Off and on since then. I tried unsuccessfully to recreate the violence of that car. My current attempt is a 900 RWHP Corvette, which certainly out accelerates.the Shelby, but is too big and too techy. I know that the engine, an LS7 will fit in a 2016 or later Miata, but will the Procharger? How about space for the intercooler?And am I crazy to even consider the combo?

And am I crazy to even consider the combo?

Absolutely, beyond any shadow of a doubt. Is it a project worth pursuing, Absolutely, beyond any shadow of a doubt! Flying Miata would be a good source of info.

Not sure if fitting the dry sump system of an LS7 is doable without a lot of extra effort. My NA Miata, which has a healthy LS3 (462 rwhp) and no power steering, power windows, A/C, or radio, is my own attempt to recreate a Cobra as it might have been built today. It's 2400#, plus or minus, and extremely raw. I love it.

So.... why not just build a Cobra?

I thought about it, but I wanted modern weather protection. One of the uses of this car is road trips, and I don't want to get soaked when it rains.

This build thread has a very similar thing to what you are mentioning.
https://www.v8miata.net/general-moto...1-2392/page21/

He did not purchase the factory engine package but rather started off with a normal V8 install then decided to add the supercharger "just because".
It is also a 1999 NB which is a couple of generations earlier than the ND mentioned by the original poster.

There are also several NC Miata's with turbochargers and nitrous that get into the 9's at the 1/4 mile drag strip.

Another option could be to go naturally aspirated and just buy a heavily built LS based engine and shoehorn it into the Miata of your choice.
If that doesn't get you excited you are beyond help.