While googling information for the class I am taking this summer (Sports Turf Mgt), I came across an article that discussed turf and trees and the inevitable conflict.
This author was saying that to truly figure out how much sun could get in, you need a computer-generated calculation due to the fact that the Earth and Sun are moving and that light availability changes on a day-to-day basis. So trimming in one manner may seem fine...for the day you trim it. But may be inadequate as the season progresses.
"No grass will grow in complete shade." Is a statement I have read over and over again. The caveat should probably read "will not grow well". Others here have stated that St. Augustine does just fine in shade.
But your photos tell a different story. Are you developing an aeration program to decompact the soil? As with all things, you can't simply deal with one aspect of a problem and expect a good result.
I'm still voting for relandscaping for enhancement and improvement of this, potentially, beautiful alle. It would be interesting to price out a relandscaping effort that would minimize the grass where it can't grow anyway, bringing in mulch, some benches and approporiate understory plants vs grow lights.
To tell you the truth, my mind boggles at the contrived situation that would promote. Sending out the message that we can create whatever we want as long as we are willing to spend enough money to do it. With relandscaping we are working with what nature is telling us is appropriate, with adding grow lights we are fighting against it.
Sylvia