I have been toying with the idea of becoming an independent researcher, raising money by working very long/hard hours for a year, then taking a year off for solely for research. This would be partially for financial reasons (Post-Doc salaries are really awful), but also because I think my research would benefit if I could pour my undivided attention into algorithm design for a year.
The biggest problem with this plan however is that in order to publish my research after a year or so of intensive work, I would need to be affiliated with an institute - even journals like arXiv require this.
This got me thinking - what actually is an institute? From the little bit of research into it I have done, it seems to be no different to a standard company, although most have charitable status and are tax-exempt or non-profit.
If other people would also like to work for-profit for a year, then for-research for a year (or at some other frequency), then a virtual institute to publish under would be quite a useful thing. In fact I'm surprised such institutes don't already exist: we have scam journals and scam conferences - why no scam institutes?
Of course if I did set up an institute to publish under it wouldn't be a scam, (there are numerous benefits I can see a virtual institute providing for members), but the idea of a on-paper-only institute is applicable to both.
If your research is valuable then you should be able to find an institute to affiliate with. If there is a lack of interest in for temporary or part time affiliations in your field (that would work with your research needs) then perhaps there is a demand for institutes more welcoming to non traditional relationships.
There is no reason why such an institute would need to be a scam as you refer to it. Find others in your situation and form an institute together. Depending on the research you are able to produce, perhaps you can attract funding at some point.