I read with amusement your article in which a psychologist and an economist tied themselves in knots trying to figure out how to persuade academics to review articles in a more timely fashion.
The answer should be pretty obvious to anyone with a knowledge of human behaviour and economics. Use some of the journals' hefty fees to pay expert reviewers for their work. By this I mean real money, not free access to irrelevant search engines and websites that no one ever uses.
Organisations I have been involved in that pay for reviews have little trouble in expediting the process. I wouldn't restrict this to journals either. The UK is plagued by a lack of reviews for grant applications. Spending a tiny fraction of the grant to reward properly those who provide timely reviews would ensure the overall process was a lot fairer, and the government money better spent.