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.