There is no single “perfect” 4 wheel alignment set up. What’s good for lower speed direction change will often compromise high speed stability and vice versa. Suspension type, ride height and wear as well as tyre choice need to be thrown in.
Better tyres and alignment from someone who knows these cars will transform the car.
You’ll be happy with any of the premium tyres after having cheapies. Rainsport, Mich PS’s, Conti Extreme or Premium all get my vote.
I don’t want to hijack the thread but may I just ask-
I have had three MX5 soft tops. Each one came new from the dealership fitted with Yokohama tyres as standard.
I note with interest that on a number of threads on here regarding tyre recommendations that Yokohama tyres rarely get mentioned
Why is this? I don’t drive aggressively, they have always given me a great ride and seem to last well.
Landsails? Just ditch them and get the best tyres you can afford.
Michelin PS for me,
New boots fitted yesterday and handling seems much better so far.
Thank you all for your comments etc. Much appreciated 
Should be good now, have/had them on both of my NC’s like them so much I had a set fitted on my daily driver too. That completely transformed the driving experience, it had Bridgestones on from new and never felt comfortable with those.
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yes, it has to be said!
tyre choice has quite an effect on the feel of the MX5 NC.
I’ve personally never known any car to feel so different with only a tyre change!
the real problem is that everyone has different a taste in how they like their car to feel.
And so there simply isn’t a go too, everyone likes, tyre choice!
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I’ll 2nd that