But if you’re travelling in the opposite direction of the rotation of the earth - east, I think; I’m having a hard time visualizing which way that would be - wouldn’t you be moving more slowly than everything around you?
I've been a trucker for many years. Not the fastest vehicle, but still relatively fast and a lot more hours on the road than the average person. I'm pretty sure that time rather shortened my life than extended it. All the sitting and the fastfood are not good for your general wellbeing. Also the fact that I grew to hate the job, was very detrimental.
This is shown by a set clock in the car not connected to satellite. If you set the clock in may, to the time on your cellphone, then drive until September, you will notice the clock in the car is behind.
The level of inaccuracy in a regular clock resulting in drift is orders of magnitude greater than any amount of time dilation you would experience.
This is the reason we use extremely high precision clocks (like atomic clocks) and then synchronize everything else with them. Even your phone's clock would drift noticeably over a period of a few months if it never synced with some network server.
The NTP protocol exists precisely for this. There are entire companies that specialize in providing and maintaining synchronized wall clocks for facilities like hospitals, schools, and other organizations.
But one's life happens in a context. If the world around you changes faster, then you spend less time in that context before it changes. Going out of the common reference frame means your life is cut short.