Is it possible to find an unpaid and "half-time" postdoc?
I know that some institutions can offer the "associated member" status to a researcher who is not on their payroll. The researcher needs to be recommended by a senior professor from the institution, who typically presents a project with this researcher to justify the request. However I've seen it used only with somebody after they had been a postdoc in the institution. 

Obviously one needs at least to prepare a research project with a member of the institution, so I think the best way would be to contact the academics in your network who could be interested in a project with you. I'd suggest to propose to work with them for free on a grant proposal, since this would be interesting for both the PI and for the institution. If you find a suitable EU call, you could even try to involve a partner in Spain which would hire you if the grant is successful.