Replaced the crumbly old cowl and a shiny new one! Easy job that I bought a wiper arm puller for. Only little complication was the wiring and fluid line in the right corner that had to be disconnected. What a difference!
Old one lifting off and falling to pieces:
Comparing the two:
Easy to disconnect, just a little hard to access:
Et voilą:
(really is flush, photo just makes it look like it's puckering up)