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.

First off I can only go based upon what you have written....so am sure that there are other variables that need to be considered. However at a high level, here are some thoughts.
First you are right that customers expect to do a full trial before purchasing. Although the intention is for them to do this during the trial period, I would anticipate that many take the trial however life gets in the way and they do not actually test it and then you are into the chasing game to try and convert them.
On the surface they are trying to mitigate their risks before committing. So, if you want them to purchase without the trial version then you need to find a way to make them feel like they are not taking on any risks. Some ways of doing this is to have them sign up with a 30-60 day full refund policy, or have them sign up and then they have 60 days to cancel without incurring any costs. These are just simple examples where the risk is shared. Right now all the risk is on you and you also have a great deal of costs to support the environment to handle these trial versions. It has to be a win-win.
As for tailoring the product for their specific needs, this needs to be a fee based service. Even if just a small amount, the customer needs to have some vested interest in finding a solution as well...so if you take on these services without charging then again you are carrying all the risk.
Hope this helps. Happy to offer some more thoughts if you are able to offer some more context regarding your specific situation.

This answer is simple: use Calls to Action (CTAs) on your site that encourage visitors to talk to you instead of trying it on their own. Pose it as a "free consultation" instead of a sales plea. If you have sufficiently sold the benefits of the features, this is not a very hard ask of visitors.

This might be something worthwhile to test with an A/B testing tool like Optimizely.

That's like asking "how do I get that fish to take my bait so I can catch him". The answer is you can't make them buy you have to figure out if your product (the bait) is appealing enough to skip the trial.

Do you have any customers who have bought without the trial? If so, ASK THEM why they did it. That will give you much better answers than the people here who are giving good, although generic answers. You need specifics about your product.

Perhaps you are asking the wrong question. The bigger question might be "how do I double my buy rate after they've done the trial."

Many good answers that I won't duplicate, however one additional thought: Have you analyzed the specific metrics around the customers who HAVE converted to paid to see how they used the product, what data they input, etc? If you can figure out what's common among companies that do convert you can then design your marketing funnel to make sure that people do those actions, for example with additional training and emails in that area.