Indesign should handle all the buttons and pages properly,
What happens when you export the page 200 only as SWF , does the button show up or is it have black box on it?
Have you created the button yourself or used the sample button ?
Please provide the screen shot of your Indesign document and the output , to know what exactly you mean "black boxes appear over buttons"?
When I export any single page the buttons look fine and the page flip works fine as well. I used the sample buttons provided by Indesign and there just simple "go to page" buttons which all work fine. Below is an image of what it looks like with the black boxes and its missing the left page for some reason. I'v went into the advances export setting and changed it to a lossless PNG at 144 dpi and also tried to use different setting like Jpeg at 96 dpi or png at 96 dpi or jpeg at 144 dpi???? IDK
I think you have bumped into a very annoying limitation of SWF architecture; there can only be a limited number of objects in one SWF file. That number is large, some 30.000 or so, but I guess you have exeeded it with that enormously large publication. Another thing that would be quite unhandy with that file is filesize. InDesign usually can´t package SWF file to small size so I guess you will have very large SWF file after exporting 350 pages? let me guess, over 100mb? It´s a pain for every end-user to download over network.
If I were you, I would export every spread as a single SWF. Then I created a new 350 pages long empty indesign document and place those spread-SWFs back to indesign, 1 SWF per spread naturally. Then I would set every SWF to be played on page load and define a poster image from current frame. Quite a lot of work but after that you can actually export your SWF with very low quality. It´s just an empty shell for you catalogue. Flash Player will load all the actual high quality page content from those separate spread-SWFs and it does it dynamically at runtime. It means that your end-user will be able start reading your catalogue pretty fast. Flash Player keeps on loading the content while users is reading first pages.
You can semi-automate that project with free SWF presenter from http://www.automatication.com/index.php?id=16
Only thing you have to do yourself is setting the poster setting. That script does everything else (exports separate SWFs, places them back to own layer etc.)
For some reason it seems that single page SWF stucks after you have used SWF presenter so you have to trash your preferences before you can export your main SWF.
If you want to finalize your publication with fancy user interface + extra features like zooming, you may want to check also http://www.edocker.com > eDocker2 Desktop Publisher.