I think the best bet for juice would be to export frozen concentrate.
And despite the logistical challenges you cite, lemons imported from places like Argentina are now cheaper to buy at Palma's wholesale market than the average wholesale price paid for local fruit, which has subsequently plummeted even further.
Except that lemons are picked for "cheap" in Argentina (and oranges in Morrocco or Valencia), industrially packaged to ports (most likely to BCN or VLC ports) and then shipped in containers to Palma.
Pick the oranges in the middle of the island: not cheap, as stated. Squeeze & freeze the juice (likely around Palma): not cheap, not even including transportation. Ship them back to the continent: probably not cheap either.
Transshipment is extremely costly and even more so at a smaller scale, and that's what we're comtemplating here.
And despite the logistical challenges you cite, lemons imported from places like Argentina are now cheaper to buy at Palma's wholesale market than the average wholesale price paid for local fruit, which has subsequently plummeted even further.