That's why Israel or Spain have such a high life expectancy with such a modest economic life, people retire there, they come while having already survived.
Life expectancy is computed by counting deaths per cohort and year. That is, the statisticians will count the number of people your age who die in your location this year, and the number of people one year older, etc. At the end of the year, they do the totals and compute that, say, 0.1% of people your age died at your location, and 0.1% of people one year older, etc.
Then they compute your life expectancy by multiplying those chances together.
People moving shouldn't affect that significantly, because this computation doesn't use the past at all. All the data comes from one year.
The big assumption there is that your chance of dying in ten years is assumed to be the same as people ten years older than you dying this year. The small assumption is that the population is assumed to be stable and countable within the present year (I suppose it's possible to work around that with more sophisticated statistics, though).
The elderly on death's door in a nursing home are not moving to some retirement community in Florida where they can DUI a golf cart all day.
The young who are depressed or have substance abuse problems are not the people who have the spare willpower to relocate so they can run the rat race in a major metro.
So your calculations for any given year are going to favor places like NYC and Florida because their cohort includes all those "less likely to die this year" people who moved there last year. So a state or region could be doing everything wrong yet still have good life expectancy because it's where people with good life expectancy wind up.
I started by assuming that since most health care cost is concentrated in the last four years of life, that's for how long retirees can affect the statistics by moving or not moving. 4 is a small number, and the number of people who move also cannot be large compared to the general population in the area they move from, so no matter how I tweaked it, I arrived at near-zero results.