Turn this upside down now, think about 100 users paying $50 a month for something they depend on, I bill $100/hr, if you can save me an hour a month I'm winning, once you have $5000 a month every month think about the next 100, keep going, sounds like your product has a use, don't make the free mistake, it's been highlighted here many times, good luck!
If you're going to have a free tier, I'd say limit it to N service integrations (3-5), but definitely make your core users paying close to the start.
If I had a need for something like this day to day, I'd definitely pay... Actually, I'd suffer for a while, then try it, then suffer again, then pay... but that's me and I'm kind of cheap/frugal. Most people will start paying once they see and feel the value.
Also, it's much easier to field requests from a few hundred paying users than thousands of non-paying ones. It's very hard to do conversion from free after the fact... many businesses have failed, burned, burned out, and left their best (paying) users in a lurch following this model.