You seem to have a Frankenstein set-up there based on no logic whatsoever.
As Magpie suggested, adding 15x8 rims on a N/A car is a problem because you're just adding unsprung weight, a big negative, for no benefit other than aesthetics.
Going back to a lighter 6.6" or 7" rim will also increase your acceleration (NA8's don't have a lot of power to start with and heavier rims/wheels are harder to rotate) and require less wear on your brakes.
The MSM/SE had the widest rims of any NA/NB, 7", because the factory deemed that wider tyres were necessary for the additional power.
Your tyres are another inch wider on a N/A car which doesn't need the extra grip.
The MSM/SE had the largest sway bars of any NA/NB, 23mm front and 14mm rear, because the factory deemed it necessary for the additional power and stiffer suspension.
The 14mm rear MSM bar is still used by even highly boosted MX5s so your 17 rear inch sway bar is WAY OVERKILL and possibly why the handling is so bad.
Why so big?
When I first got my car, I remember talking to Richard Larsen of MX5 Plus about handling modz - he warned me that it was a very slippery and complex slope because Mazda designed a very light car that handled exactly how they wanted it to handle. Changing any single component would require changing virtually every other component to correct issues introduced by the new mod - and he was right
Suspension and handling is very much a "black art" to most of us and research is your best tool here - do some searches on what combinations other people have and are happy with (you'll need to filter out those who rave about how good their new cheap shocks are after replacing their 25 year-old OEM shocks since ANYTHING will feel better in that scenario). See MT.net for some good suspension tips/combinations - if anyone has suggested a crap combination it will have been shot down mercilessly and if you're lucky, they may say why they're so bad. Contrarily, good suggestions are usually backed up by others. Whatever you do, DON'T simply create a post there unless you include the details of your question/build and include some research you've already done - they don't tolerate newbie's who can't even be bothered to do some research on questions already asked and answered a million times before (the longer I've been on that site and the older I get, the more I agree with that attittude).
If you can afford them, consider MCA Blues shocks and go back to a stock rear sway bar.
MCA can build your shocks to your preferred specifications - you wont just be hoping that your rebuilt bilsteins and king springs are compatible for your needs (and each other).
