i noticed a math error for the 62yo. 18.9 years times 12 months per year equals 227 month not 277 months and that times the $1744/mo equals $396k (rounded) which refutes this argument as that difference is significant. if you take the 62yo out to a death at 83.3 then the number becomes $446k (rounded) which still shows significant difference.
Right you are. My bad.

It's about a 9.5% difference. Not trivial.
Better plan to living longer than shorter.
Now I don't know how to think about this. I'll have to, um, think about it some more. Dang.
Thing is, at 62, you make your decision not knowing how long you are going to live, so you have to use the mortaility table and assume you'll live to 80.9.
But when you hit 70, you
aleady know that you weren't one of the unlucky 62 year-olds that died before 70. Now we're in the "Bob Barker let's make a deal---do you want to switch doors" territory. And 95% of people get it wrong here, so there's a real good chance that my reasoning here is wrong. double dang.
For those people who are still alive at 70, they now know something that they didn't know at 62. And, just like the "switch doors or not" people, you can change your mind based in the knowledge that you now have.
You can change your mind, return the money and re-file, and have your cake & eat it too.
I haven't run the numbers, but I stongly suspect that the optimum strategy (if you want to do this) is to start collecting at 62 and re-file each year until 70. Each year you can take advantage of the new thing that you now know (that you didn't die), and reset to the new higher amount.
Personally, I wouldn't do it though. I still don't like the figures. Even at 0% earnings rate and 3% COLA, my break-even point is 85--which is already beyond the age 70 life expectancy of 83.3.
Any earnings above 0% pushed the BEP even further out. 5% (with 3% COLA) pushes it past age 100.