Well as an author and musician who is using a free distribution model of publishing myself, yeah I do have some ideas.
1. Ask for money up front.
2. Ask for voluntary contributions.
3. Provide extra service (support, for instance) to people who pay.
4. Capitalize on the advantages of free distribution. File sharing is free advertising to people who know how to use it.
5. Make it difficult to copy.
The differences between all of those methods and restrictive copyright models of distribution are primarily that they require you to have a relationship with your customers to a level at which they will willingly compensate you for your work (keeping in mind that it is not only existing product for which they are paying, but the possibility of future product as well); and that it becomes your responsibility to ensure that you are compensated, rather than socializing that cost through government enforcement.
I'm not sure if the sort of work you do is comparable, but have you ever heard of the humble bundle? It was a package of five games released to the public at whatever cost they were willing to pay - as little as one cent. But the average payment, last time I checked, was about eight dollars - and the companies who released the games made, individually, more than twice what they had made from standard, fixed-price sales. The total amount raised is in the millions of dollars.
If people like what you do, they will give you compensation if you're willing to ask for it. If you charge a single rate, then those who think that rate is too high aren't going to pay you anyway - but they will probably still use your product because, like it or not, file sharing is here to stay. Last but not least, you can always call people out for being jerks if they take without giving. I think that in the absence of state-enforced copyright, communities would naturally develop means of ostracizing those who violate their standards of the fair use of creative works. People resent being told what to do under the threat of force, so resisting copyright law (which is acknowledged to be absurd, even by IP advocates) has become a badge of honor in the tech community. If compensating creators were a matter of choice and courtesy, things would be different.