The movement of trade from the Baltic to the north sea/atlantic really hurts them in the long run. I'm not terrible sure how the Hansa can adjust for it.
They wouldn't really need to. The overall volume of trade would still be enough to sustain a fair amount of prosperity, and controlling access to the Baltic would ensure a lucrative business in timber, tar, grain, wax and flax to markets in the West hungry for raw materials. The League would not be a great power, but it wasn't terribly well suited to that role anyway.
The problem is the nation states. There never was anything like a unified Hanseatic identity. Cities of the league could be subject to kings or territorial lords, self-governing or subject to external meddling. It was not a problem within the legal framework of medieval government, but no modern European state would willingly accept that degree of independence in a city. To have it continue, you need a huge change in how the countries surrounding the Baltic and North Sea are run, and I don't see how you get that without changing pretty much all of European politics.