I don't know how I missed your question, but please forgive.* :?* Though I'm not an arborist, I am a tree enthusiast.* I agree with your arborist about Norway maples.* Most arborists call them junk or weed trees.* They suck up all the moisture from the soil with their massive roots and it's nearly impossible to get grass to grow under their canopy.* You could do a soil test to see what might be missing from your soil for your turf, but keep in mind that whatever you feed the turf that covers the roots of the tree, you will be feeding your tree.* That might not be a good thing for the tree.* Here's some sites on how tree roots grow, turf and trees and how to mulch trees.*
This site has some helpful info on trees.* It doesn't have pretty pics, but loads of other helpful stuff.* Here's the species of Norway maple aka Acer platanoides.
You can read about the selected cultivars here to see if you might be able to id exactly which ones you have.
Hope that helps,
When weeding, the best way to make sure you are removing a weed and not a valuable plant is to pull on it. If it comes out of the ground easily, it is a valuable plant.