I'm not familiar with the study mentionned, but i don't understand why, in theory, the southern states couldn't lower salaries to have productivity gains ( since pay raises have been the major reason for the loss in the first place).
(note especially the ludicrous 27% "natural rate" of unemployment for Spain predicted by standard economic models cited there)
Ordinarily the problem would be solved by de-valuing the currency against the more competitive economies' currencies, but with the Euro that's not possible.
So the best way in practice would be for the more competitive economies to incur some inflation, say 5%, for several of years so that the less competitive ones can stay at <1% and restore competitiveness that way.
Unfortunately this is politically impossible in the Euro zone today, hence we have 25% unemployment in southern countries.
i just realized another big difference between the traditional devaluation/inflation solution and the wage reduction :
In the first case, savings and capital in general are affected as well, whereas in the second only workers are.
So i guess wage reduction would restore competitivity but would also increase the inequality in the country dramaticaly (unless you dramaticaly increase the taxes on higher revenues and on savings as well).
Another thing is that if a country changes its currency to be able to devaluate, you can be pretty sure that all the savings will immediately leave the country's bank and convert to stronger currencies.
Also, there's more to productivity than salary levels. You also need to factor in education, experience, access to capital (for tools and machines), infrastructure, proximity with suppliers ot clients, administrative overhead, etc. At least part of that will need to get funding (ideally by the EU).