We always leave enough time for the transfers on these types of flights. The flight mentioned in the article leaves a whole night as transfer time. When searching with this method you might actually discover routes that are 1) cheaper and 2) you were previously unaware of them. If you like the stopover you can extend the time, as the prices of these routes are likely to be similar +/- 3 days.
Tough luck. You will have to rebook and likely pay full price.