When we purchased our house from the previous owners, they had installed a retractable awning over the patio. My first instinct was to remove it, but I'm glad I waited - it's great at shielding us from harsh afternoon summer sun while allowing us to retract it and enjoy uninterrupted views and terrific light as we choose. As I looked into upgrading or replacing it (it's over 20 years old and starting to show some wear), I've read that some retractable awnings are built to handle light rain (I had always heard that you should retract them at the first sign of rain). Depending on how mild your climate is (light afternoon showers vs. torrential wind-driven storms), that might be an option. That said, be sure to check out the safety factor of grilling underneath whatever option you decide on.

I also recommend talking to a good landscape designer as your challenge sounds like one that many folks struggle with (creating covered outdoor space without losing natural light). We're in the design phase of our renovation now (also north facing backyard) and were originally completely opposed to a covered porch off the back (for the reasons you specified) - having now seen a couple of architectural models showing the impact on light with a partially covered structure, we're reconsidering.

*Also, I'm completely jealous of your gorgeous trees! What a dream backyard!

Perhaps a pergola would work well for you. Here is one we did for a client:

Upscale Observatory Park Interior Design: Exterior · More Info