Yeah. I'm adding Porsche parts now...  a.k.a the GT3 Mustache vent.

My original plan was to cut out vents like pictured in this forum thread https://forum.miata.net/vb/showthread.php?t=679801 . Had templates made and everything but was starting to doubt if it would have any effect on cooling. Plus it's hard to get a good finish.
While looking for a new front spoiler I found a pic of a NC with this mod and it looked awsome:

The OEM vent can be had for under $40 https://www.5150motorsport.com/997-gt3-front-bumper-air-vent-997-575-327-90-01c.html

Despite it's narrow profile it flows a lot of air and have proper aerodynamic louvres.
The flange around the edge will also cover any minor mishaps during cutting.

I started by taking a look under the bonnet and was surprised to see that it was not the usual rounded frame support like found on the NA/NB and S2000. The outer and inner layer is glued together in the dimpled parts. The vent is high enough to  protrude trough the inner layer.

I used a lot of time trying to find the optimal placement. If its oriented for looks which would be in the front part of the hood it doesn't seem to have any effect as it will be placed more or less in front of the radiator. There is also a lot of components blocking the air flow located over the rad so to avoid air needing to reverse it needs to go further back.

I ended up having it oriented as illustrated above. Without the battery relocation everything would be blocked. Optimal would be somewhat higher up , but that would place the vent all the way up to the bulge in the hood.

I covered the engine bay before I started. I decided to do the cutting with the hood on the car as there is a lot of measuring and cutting from both sides making it easier when it can be flipped back and forth.

Settling for the correct position before cutting took ages. I used strings to get a horizontal and vertical reference. The hood latch is perfectly centered as well as a small hole on the underside at the other end.

The eBay seller that sold me the vent said to use the underside of the vent as a template. Terrible advice since the vent expand further upp against the flange.  Use a piece of cardboard and make a template that is perfectly flush with the underside of the flange. That would have saved me a lot of time.

Since the 997 hood is more curved than the MX-5 I used a heat gun to level it out :

It worked, but I applied to much heat on the front and managed to melt and deform part of the front lip. This might not be necessary as it could be possible to just force it in place by tightening it from the underside of the hood.

For cutting I started with airtools which was hopeless. 6bar from the compressor and it was not able to cut the aluminium. So I switched to a proper angle grinder. Worked great, even in curves.  Remember to use a lot of tape surrounding the cut as the tool will make marks if the cutting wheel bottoms out.

First cut. Cutting trough both layers at once worked out great.

Many hours later with gradually widening the cut for fitment. Did some hand deburring. Also applied some touchup paint on the edges.

For mounting i used body panel screws and clips. The clips was bendt where needed to press against the underside of the hood.

Vent sits flush with the hood. No distortion of the hood itself.

Finished. Cut out a healthy chunk of the sound deadening mostly in front of the vent.
Results:

It turned out ok I think.  The curved edges does not blend in that well. Painting it would help.
But for extracting air I think it will work ok. When parked and the fan kicks in hot air is blowing straight out the hood. But only on the side where there is a clear exit path for the air after the battery relocation. On the other side above the airbox no air comes out. We will see if it keeps the car cooler on the next trackday.