Do the Triunes really depend on the North Sea and the Baltics though for both its economy and state security though? Even with the inclusion of Amsterdam and the rest of Lotharingia into the Empire, I still think much of the focus remains around the Channel and its surrounding territories.Maybe his next big target will be the EOTN. To secure the North Sea, Scotland must be secured too. If he wants to make inroads in the Baltic, the EOTN must be taken down a notch or two.
I think Frame's reasoning is more sound if Henri or Louis do want to invade Scotland. A weaker EAN and an annexed Scotland does mean that the Triunes can reign in Northumbria as well as satiate the rest of English nobles by making Scotland part of the Kingdom of England similar to Lotharingia went to the Kingdom of France.