404 would waste any IBLs.
But if leaving them as a 200 and serving a standard 'event over' wording means thousands of dupes, I think this would be even worse. IMO it would be preferable to leave the page as is rather than delete/replace the content and just leave boilerplate and template.
If you really, really can't do a 301 to another useful page then I think either a 404 to clean out the index or doing nothing would be preferable to filling the index with duplicate content, whether linked to or not.
But, like others, I don't believe that you can't get the issue fixed. Hiring a top notch multi-skilled programmer with the requisite coding, platform and SEO knowledge for a day or two will not cost anything like six figures.
You said the header response of 200 is being sent by one server then another displays the content. So send a different header response and different content. Whatever routines are running can be analysed and changed.
Can you not contact the people who built the system?