Sounds like you are on the right track for sure. I would do a 3 mile trail run with some moderate hills instead of 3 miles on the treadmill. Also, during the other run, maybe do some intervals (for example, 5 x 400 meters or 5 x 800), without fully recovering between intervals. For me, it kind of simulated the oxygen deprivation you feel at altitude. You get used to the discomfort and learn to push through it.
You'll want to get some 12+ mile hikes under your belt, at altitude, with 4000+ feet of elevation gain. Lots of options in the San Bernardino mountains. The closer to your Mt. Whitney hike the better! Getting used to laboring at altitude is really important.
If you haven't hiked Mt. Woodson yet, I highly recommend it! It's about 7 miles round trip with ~1900 feet of elevation gain. I hiked there last month on a family vacation to kick off my own training for this year's Mt. Whitney hike. Try to avoid hiking there in the heat!
