Best way to introduce our free version limitations?

On one hand, I totally sympathize with how you feel. It's scary to charge for things, and to your users out of the thing you built. But it's important to realize that simply charging for your product isn't the same as "forcing" things on your users in a bad way.

When I think of an overly forceful or pushy product, what comes to mind are barrages of popup modals, countdown timers, etc. In other words, products that can't get me to buy via the value they deliver, and so instead rely on obnoxious gimmicks. I don't think of products I love that simply have paywalls. Those are just fine.

My advice is to:

1. Be upfront about the fact that this software is not free. Don't let people invest a ton before you tell them. Don't bait and switch. You don't want your payment screen to come as an unpleasant surprise in the middle of someone trying to use your tool to get work done.
2. If your conversion rates are low, go back to the drawing board: talk to your customers to try to understand them better; learn about their professions, needs, and use cases; and improve your product accordingly. Get things to the point where customers are actually happy to pay for the value they're getting. Avoid simply over-optimizing your signup ask.