Dilemma: I have information that is highly valuable to several PE companies. How to monetize?

Hey guys,

I hope somebody has some useful insights. TL;DR: I have information that is highly valuable to several PE companies and I would like to sell this information. Is it even possible to get in touch as an outsider? 

Without disclosing what the information is, here is made-up example to illustrate my case. Certain industrial CAD software has a super-strong customer lock-in. Industrial companies have been using the software for decades and can’t suddenly stop, because of backward compatibility. Other software won’t support their existing drawings—and redrawing everything would take "millions of hours". 

Let’s say I know several people who work with this software, they absolutely hate it, and would love to switch to a competitor. They don’t switch for just one primary reason — let's call it reason X — which is pretty easy to fix. That reason is not backward compatibility, which seems like the obvious answer. 

The competing software is owned by a PE fund and they are very obviously unaware of reason X. The insight is very valuable – “if you solve X (and here’s how), you remove the main blocker stopping new customers from switching to you”. I understand it sounds strange, but it doesn't make it less real or less valuable.

The info is completely legal—no non-competes, no stolen IP. I know it sounds a bit weird, but it’s a very narrow niche and a niche kind of insight. My information is not about CAD software at all, but you get my point. I would like to get in touch and sell the insight.

1. How realistic is it to get in touch as an outsider?
2. How do I even contact them without being lumped into the “spam / scam / annoying salesperson” bucket? I’m pretty sure cold emails or LinkedIn won’t work—those guys get flooded with spam already, and this is a pretty unusual pitch. On top of that, there are only a handful of companies for which this info is both relevant and extremely valuable. So I can’t just spray 2,000 messages and hope that 3 people reply.
3. How to structure this so that this is safe from the PE company's perspective, and I don't get screwed over?