I owned a 99 10AE which was a total loss. I have it's hardtop. My wife has a 2001. I pulled the frankenstein bolts from my 1999 and put them in hers. We plan on using the hardtop on her car.

Besides the frankenstein bolts, is there a way of adjusting the top so that the rattle is not so bad?

If I need the side striker kit, do I need anything more than https://mossmiata.com/hard-top-side-striker-kit ? Is there a bracket right under the place where the side striker would install?
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You need the side striker kit from your link.
to reduce rattles, you need to adjust the latches so the top fits snug.

If you look on the latches, the arm that grabs has a bolt in the middle, which is held by a plastic cover, pry open that cover and turn the bolt, it will make the arm longer or shorter. So adjust until top fits nice and snug.

 

strikers and also you can try to adjust the anchors where the Frankenstein bolts are

 

https://www.miata.net/garage/latch_adjust.html