I know it sounds counter-intuitive, but I would stop running and focus all of my training on walking uphill quickly. Find a nice, long hill (or Barr Trail itself) and just do repeats if you have to. Even better, ff you have access to a treadmill, set it to 15%, turn on the tunes, and get walking. Focus on taking shorter steps but at a higher cadence. Also practice breathing in on one step and out on another. That helps a lot above treeline.
For the vast majority of folks, after you take that turn onto Ruxton ave, odds are that it would be in your best interest to walk the rest of the way to the top. Many folks force themselves to run large chunks of the first few miles only to wish that they had not wasted so much energy getting up Ruxton once they find themselves above treeline and are slowed down to a stagger.
Also, don't equate walking with being slow. Last year I walked from half a mile before Barr Camp all the way to the top, covering the A-Frame to Summit section in 56 minutes.
--john