Thanks for all the comments! Truly appreciated. They have given me a lot of food for thought.
I’m currently running stocks, but I have my eyes on quite nicely priced low mileage original mazda bilsteins that I’m also considering (yes like everyone, I want new toys to my ND and swapping those would be doable in my garage, ARBs are a different story). They won’t solve the the body roll issue, but at least general consensus seems to be that they are better than stock and with 300€ (with springs and 10k on them) they seem like an awfully good deal in my eyes. Also did test drive 2016 with bilsteins when I was looking my MX-5 and I have nothing to complain about the ride. Although I can’t say I was very analytical about it or didn’t even know what to look for in handling back then. But I do remember that they weren’t harsh in a way that would bother me which was always the number one thing that always impressed me on MX-5.
After doing some anti-roll bar research on my own (know good amount about motorcycle suspension, but cars are relatively new to me). I also realized that they also harshen the ride especially uneven bumps because left and right act more like a single unit. And this got me a bit worried.
I actually live in Finland and uneven bumps are especially the problem on local back roads where the frost damage creates all kinds of havoc to roads (so potholes, bumps, cracks, patches, patches on patches and so forth). If there is a bump, it’s almost guaranteed that there isn’t a matching one on the other side. This is especially an issue on gravel roads that you simply cannot avoid here when on the hunt of those lovely b-roads. Also I drive my car all year round, and roads packed with snow and ice are a completely different beast for suspension.
So suddenly anti-roll bars don’t seem like such an optimal choice in my mind after all… It feels like I would be substituting body roll for maybe another kind of annoyance. Or am I reading too much to this? I have a nagging feeling (based on my experience on bike suspensions), that changes are far more subtler than I think they will be.
On the other hand I’ve driven some pimped up tuning bimmers that had zero body roll and you could feel every crack on the road on your spine, though these were the regular “youth tuning”-cases, where low ride hight and the cheapest coil overs was the thing, not necessarily how the car actually handles. Also driven one track optimized car (Porsche 944) and that is definitely not what I’m after but that was a street legal racer so don’t think that’s a good comparison point either. Also, I hated my friend’s stock Octavia Combi III due to its harsh, non-compliant suspension on sharp bumps (seems to be issue in relatively new Skoda/VW in general). This harshness is something that MX-5 is completely missing. With stock shocks you know there was a bump you can feel it but it’s not sharp, it’s just there. Those sharp harsh clunks are what I’m desperately trying to avoid.
Also I know lowering kit would firm up everything and help also with body roll, but as I live in the countryside, dropping the ride height is a bit problematic move. I really do need those “ugly” centimeters under the car. Otherwise this tuneup has a possibility to be a very expensive one. Shocks + springs 1000€+, redoing my road so I can get my MX-5 to garage without leaving the exhaust behind…. 10 000€+ 
And sorry for being such an awfully complicated case
My use-case is a bit peculiar one, and there is a distinct possibility, that it’s perfect just as it for my use, but daddy needs new toys for his roadster 
(and yes I know the MX-5 is probably the least practical car for me, but I decided year ago that I’m done with boring practical family cars. Haven’t looked back once, so it seems that once again Miata Is Always The Answer
)