After your fertility experiment, perhaps a big dig-out, and then replace the soil with some good stuff.
I love to dispense advice (lol, I'm a mother and a gardener...advice comes whether you like it or not!!)
- I think the elm in the driveway is down-the-road a big problem. You may want to consider taking it down while it is still small-ish. I can see you had to take one down already.
- I'm also not a fan of the ivy monster. If you are not ready/willing to dispense with it, maybe keep after it so it looks tamer and neat.
- Fruit trees could be interesting, but consider the apples (or whatever) falling onto your driveway...can be messy. But if shade is what you're after, maybe some crepe myrtles (they come in all heights and colors) and it I'm guessing you are somewhere in the south? Zones 7 and above are good for crepe myrtles.
- In the strip that is always in the shade where nothing grows, consider a shade-loving ground cover like pachysandra, or ostrich fern, or a carex like 'blue zinger' or 'evergold'. There are a ton of carex out there, so you could find a color and height that you like. ALso maybe vinca major (also referred to as periwinkle myrtle).
Good luck :-)
RE: The Strip by my Driveway