Good report, Alyssa. The icy spot at the cables was a good place to turn around, given your total time on the trail. Had you gone to the summit, the trip could have become an epic.
You can go back to Whitney this year, if you want to go for walk-in permits. There are lots of no-shows, and their permits become available at 11 AM at the visitor center each day.
Next time, get in some acclimatization. I think your "gungy" feeling was AMS. Stay two nights at Whitney Portal, or better, Horseshoe Meadows before the next hike. That will help greatly.
And your water intake and output was pretty excessive. All those stops surely slowed your progress. I'd cut the drinking in half.
If you prepare by doing several long hikes in the several weeks before Mt Whitney, I think the Whitney experience won't be as bad.
Good luck!!!