Maybe you could approach some experts in the field, humbly present yourself, briefly explain how your tool works and how it can make their life easier, and ask

Maybe you could approach some experts in the field, humbly present yourself, briefly explain how your tool works and how it can make their life easier, and ask them whether they'd consider a no-string attached test run. If it's a real niche field like you said, they probably won't get swamped by this kind of emails very much and will get curious. Once you make a few fans, you could ask whether they can spread the word, or, if they're really into it, they'll do it for you on twitter and such.