Don’t do it.
I did something similar for 6 years and can confirm the research that indicates it lowers all measurable forms of well being. I would gladly take a pay cut to avoid what you are considering. So please be aware that I am biased.
With that said, numbers wise, your math seems off based on what I recall - gas isn’t the only cost - having done this - cars get burned up every few years. I remember doing oil changes monthly and that was pushing my luck.
The federal government uses 50 cent per mile for total transportation costs - the depreciated value of the car, repairs and gas and so forth. Doesn’t count for tolls but is a fair enough representation for this exercise.
Using the government number (you will want to double check my math):
Your current commute (50 weeks) = 9450 a year or $4,725 in current annual costs
Your new commute (50 weeks) = 31,950 or $15,975 in annual costs
And this is before extra outsourcing (eating dinner a home would be a challenge with this schedule) and simply no extra time to plan other frugal moves. It is also before the extra gross income required to generate the additional $11K in transportation expenses - probably about $15K raise would be needed to cover it.
Sure, a used car can lower costs but with 30,000 annual commute miles a bit for errands you will easily add 100K in miles to a car every 3 years.Even a new car would be hard pressed to make it to the ten year mark with 333K on the odometer.
If we invert the question and I am reading your use case correctly, we see you would add 100 minutes a day or 500 minutes a week to the drive. That is over 8 extra hours. A full extra day of work.Every week. All year.
You clearly have a high work ethic. I bet you a lunch that if you switched your schedule to work at your current job six days a week and did so consistently that in just a few years that you would be able to get a $500 raise or a new job closer to home that has that raise - or more. And, unlike the commute, the new skills would be readily transferable to future jobs and would result in higher pay for decades. A super long commute will deliver you to work exhausted and less productive simultaneously lowering future raises and increases the likely your salary will go to zero in some future lay off.
PS - I switched up to a new job closer to home for a pay cut. With the extra time I am getting a graduate degree at night and I still have more free time then I did with the long haul. My guess is that the degree will eventually yield more income than a long commute. Plus, I can pop out to the bathroom to pee during class which wasn’t an option on those long drives which always made those last few miles occasionally harrowing.