Sounds like taking a small amount of chemical should do the trick. I did find an article today on the recommended water sources on the trail. Thanks for all the above advice!
Be sure to try out the chemical at home, first, if you have not used it before. If it tastes too awful, it may discourange you from wanting to drink water.
I agree with WB that the Whitney main trail has become a uniquely impacted area (that may not remain in line with the pristine reputation of high sierra water quality due to the ubiquitous WAG bag presence.)