This is a classic issue of where your customer base has broadened to the point where your users are not coming from a point of high education/information about your product and free software models of business.
As difficult as it seems, you need to be patient and spend some time educating this new segment of your customer base. If people are downloading the software from a website or source you control, make sure to have a big, bright, and happy notification that explains how your product is supported. I'm suspecting that your software is available from many sites you CAN'T control, so it might behoove you to have a big, bright, happy notice as part of a splash screen during install or startup. In your case it would be completely inadequate to expect people to read any "click to agree" dialogs, and you might simply need to put what amounts to a banner ad for your phone support in any help menu or dialog.
As much as we hate the ubiquitous advertising in our products, you have not simply an interest, but practically a duty to inform your users the specific details of how you perform support. Make sure that anywhere your support number is mentioned, you also mention your fee-for-service or contract support model so you can weed out all but the most stubborn non-readers.
If you have a media person, or a team member who generally responds to postings on message boards, make sure that they are sending a consistent, measured response that avoids emotional flags and simply states your company's position and your business model.