As an indicator of preparedness for hiking Whitney I have a couple of old saws (adages) that I find work well. They both assume a training program that has been underway for at least a few months. To be properly prepared you must meet the requirements of both saws.
These saws are based on your target hike’s profile. For Mt. Whitney, main trail: 22 miles, with 7,000’ elevation gain - you actually lose altitude at several spots along the way, so the elevation gain is more than the peak altitude minus the trail head altitude. You lose/gain this elevation going in both directions.
1. Your weekly total should exceed your target profile. This is the easier of the two conditions. For Whitney, this means that each week for the four weeks leading up to your hike you should be hiking a total of 22 miles, with a total elevation gain of at least 7,000’.
2. You should be doing at least one hike/week that is equal or greater than 1/2 (one half) your target profile. So, for Whitney, at least one hike/week that totals 11 miles with at least 3,500’ elevation gain. You should have been doing this for the previous 4 weeks.
So, with your current status, you need to increase your big hike by 5 miles, and 1,600' elevation gain. I would also advise adding additional hikes instead of the treadmill to get a total (minimum) of 22 miles/week, with 7,000' elevation gain.
If you are hiking near sea level, you should also consider increasing your speed a bit.
Let us know how it goes.
Good luck.
