Actually, I know of at least two people who are working on that exact concept. Seems pretty obvious to me. The Westfield is similar, but it doesn't use the Miata control arms or subframes.
I think $10-12k is a plausible budget for adding an LS powerplant to an existing Miata. Go all Challenge on it, and you can knock some more off it. That's assuming you use used parts and you're good at hunting down deals, of course. The little odds and ends can add up in a hurry, and it's more expensive to do the conversion to an NA like this one than an NB due to changes in the fuel system and gauges. Plus the stiffer chassis of the NB is beneficial, so it's worth spending just a little more for the newer platform. Besides, you'll get more for the parts when you sell the engine, transmission and rear end.
When we do a conversion, we use all new parts. It's basically a new car, despite what the body looks like on this one. It's got the engine from a 2010 Corvette, with a hot cam that gives it an extra 50 hp - and the engine carries a two-year warranty. The transmission is the same basic one used in the 'Vette. Assume we start with a $10,000 Miata and we do $35,000 worth of work to it. The end result has 50 hp more than a 2010 Corvette, weighs around 600 lbs less - and the total cost is $10,000 less than a 2010 Corvette convertible. Look at it that way, and it's a bargain.
Do they handle like a Miata? They do! I'm pretty quick around our local track. In fact, before the 2009 Open House, I was the fastest Miata driver to get around the track in my Targa car. This is a kart track that rewards handling more than sheer power. The first time I took Elvis - the slow V8 car, remember? - out, I went 2 seconds a lap faster than I did in my own car. Elvis is a street car, not a caged racer. They shared the same AFCO suspension, but still. We've also taken it autocrossing at a Corvette autocross, and we set FTD by something like 5 seconds. Yeah, they still handle.
It's not exactly like a Miata, though. The first time I came on to the fast sweeper on the back of our track, I hit third - and the back end lit up and stepped out. I came down that hill on full opposite lock as I rode it out. Other Miatas don't do that. My Seven doesn't do that. The turbocharged Westfield doesn't do that. So you do have to show a little discretion with the loud pedal. At Laguna Seca, it's magic - you'd be amazed at how well the diff works. But yes, it's got a very high power/weight ratio so you have to treat it as such.
I used to be skeptical about these things. I'm a complete convert now - and that's why I'm building what I am in the garage
And as for the desert pink? I'm a Land Rover guy. This is what I think of - the SAS "Pink Panthers".