You would want to hinge the purchase on a key feature that gives you a competitive advantage - and that is not fully incorporated in the trial version.

I have advised SAAS Product Managers and your dilemma is certainly a shared one - getting customers to pick a) paid over free/basic/trial and b) getting them to pick the most lucrative package of the paid ones.

If as you say, the software is complex, then we need some interface-based simplicity: try explainer videos for starters.
http://www.powtoon.com/

So in sum - a friendly interface, and feature-based price marketing are two good places to start.

Happy to have a conversation with you for further details.