Welcome to RTA!
I see a good pattern in your plan, similar to the way my hubby and I would plan. I will let someone else chime in about your day 6, though, as I've never been to Death Valley. Lone Pine is just a little town, and going back to Las Vegas probably doesn't make a whole lot of sense. However, others may have different ideas.
As far as a good place to stay in LA while doing up Hollywood, Universal is concerned -- there are some nice hotels along the coast if you want to stay there. There's also a Best Western and a couple of other places close to Universal, or stay in the Burbank area. (There's a decent Holiday Inn there, as well as a Marriott, in Burbank. Be careful about making any reservations in "North Hollywood", as some of the areas can be questionable.)
Buy your national parks season pass at the first place you go -- in your case, Grand Canyon. Grand Canyon, Sequoia and Yosemite all charge $20 entrance fee (good for 7 days only at that park), and Zion charges $25 (also good for 7 days), so that $80 at Grand Canyon will be well spent and saves you $5.
Donna