It's an interesting one for sure. The realistic answer is... none of them
You really can't get a mid-engined feel without the engine in that place, simply due to the physics involved.
That said, the cars mentioned so far - MX-5s and the 86/BRZ - are probably about as inertia-free and nicely balanced as any car from the past three decades, and particularly once you start playing around with modifications the way they behave is about as close to the dictionary definition of "handling" (that is, responding to exactly what a driver is asking the car to do) as you'll get. Still not mid-engined in feel necessarily, but with similarly few vices as a good mid-engined car in terms of behaviour. Plus that extra element of stability you get having the engine in the front rather than ahead of or on top of the rear axle.
BRZ/86 is off to a better start than a stock Miata, but in stock form both have their issues. The BRZ/86's are the tyres, because while the low-grip strategy was admirable, it makes the car nervous when grip is already low (such as when it's raining), and the rest of the time it muddies the steering feedback as those tyres just didn't have the right structure to deliver feedback as they should. Sadly, I've not yet driven one with decent tyres so they've all been "imperfect" so far. But otherwise they're great. Low CoG, nice balance, and a very stiff structure so the suspension can do its stuff. And "my" 86 Blue Edition had factory Sachs suspension which also gave it the best ride of any 86 I've driven - early ones could be just a little firm.
There are a few gens of MX-5 obviously so there are different faults to each... NA/NB it's chassis stiffness. They improved over time, but it's definitely my least favourite thing about those cars, as it corrupts precision and makes the thing feel like it's falling apart on rough roads. I've only driven mk3.5s as far as NC goes so can't comment first-hand on pre-facelifts, but I'm led to believe their main issue is poor steering feel and inconsistent spring/damping front to rear. 3.5s are better, so I'd say weight... but it's still lighter than an 86! NDs, it's steering feel and not enough body control. The both combine to make a car that's actually pretty sketchy when you really get up into it.
Good stuff? NA/NB it's steering feel (the earlier car being subjectively better for me, typically on narrower tyres), and wonderfully friendly balance so you can huck it about like mad whether you're on the road or on track. NC, good balance again, and what feels like better structural stiffness than any of the other generations - it's definitely a more "solid" car. Probably the best basis for a trackday car as the longest/widest. ND? Feels very light on its toes, and at low speeds the roll makes it feel much like the NA - albeit without the same nice steering or friendly tyre breakaway.
The surprising thing though is that in pure handling terms the best MX-5 I've driven was an NC, tweaked by BBR. They did relatively little - Goodyear F1s (I think), a decent spring/damper combo (not coilovers) and thicker anti-roll bars. Only drove it on the road, but it had the best balance and most progressive grip of any MX-5 I've driven. More so than BBR's own NDs I've tried (though with very simple tweaks they're way better than stock too). Both pictured...
My personal preference, particularly on the road and with our road conditions over here, is for stuff that isn't too extreme. I've no great desire to try an MX-5 on semi-slicks as the joy of those cars for me isn't outright grip but their balance, and when you move one slider the other one goes down (at least until you're making big power and have a track to exploit it). So I like the way they do things, and the best ones are those that enhance the characteristics already in the cars.
Same would go for the 86 I assume - though the elephant in the room here is that while I've no great issue with the old 86's engine in most conditions, the ND's engine in particular (and its gearing) is better suited to making the most of the chassis.
While I'm here, a few other observations:
Until the ND2 came along, the best modern "MX-5" was the Abarth 124. The chassis felt a bit stiffer, the suspension less floaty, and the extra torque made it even easier to play with the car's attitude at lower speeds.
Most of my mid-engined experience comes from Boxsters and Caymans. They're lovely things to drive in general, probably some of the best sports cars at any price point in fact (and from the ones I've tried at least, I tend to prefer them to 911s). But I do have more fun in MX-5s and the like, mainly because even a basic Boxster these days goes like stink so there's a limit to how much of its performance you can use on UK roads. I did get a chance to drive a 987 Spyder on road and track last year though and that's probably one of the best things I've ever driven - even ignoring the engine/transmission, which is fabulous, the balance, adjustability and steering feel in that car is top-level stuff.
Ditto the Alpine A110. Much "lighter" feeling than a Boxster/Cayman (and not just because it
is lighter) - it's a very delicate thing and floats over a road surface (without feeling all at sea) but if you want to talk "balance" in a Best Motoring sense where you look at the way everything you interact with contributes to the whole, that's also an all-time great.
Caterhams? Brilliant, but not mid-engined feeling at all. Ultimately nose-heavy, most apparent on the slim-tyred ones (though those are still my favourites).
Going back to the 86 briefly... if that's any Porsche, it's not close to a Boxster but a 924/944, ain't it?...
... Can't wait to try it on even GT sport or GT7!
