As an endurance marathon runner, I feel your pain. I failed on an attempt with my father a couple years ago. I am beginning to think more and more that unless you can really acclimatize fully (meaning slowly, hike high camp low) there really isn't much you can or should even bother trying to do. Maybe you would have been better off resting than hiking at Horseshoe Meadows.
So unless you have a lot of time to use on a vacation, I'm convinced that crossing your fingers and taking Diamox is the best strategy.
Several schools of thought on that. Acclimation studies generally show that in expedition-style mountaineering, the climb-high, sleep-low strategy is the way to go. But that's really for approaching or passing the 18-19K' level where the body just refuses to acclimate long term. "Low" is a very relative term. Most folks on Whitney, or any other American Fourteener, usually find the going becoming difficult at 10-12K'. The goal is to only get to 14K'.
I've found that if I try to go from the lowlands to 14K' with one or zero night's sleep at altitude, I'll feel it. Two to three nights is perfect for me - no AMS symptoms at all, but still can't move anywhere near my normal lowland pace. Five to seven nights at elevation, and I'm feeling almost normal while I hike high.
But then, just as I think I'm really, finally in shape to tackle the fourteeners on their terms, it's typically time to turn around and go home. Dammit.