Hard eggs at altitude

We now live at 7,000 ft. But for decades before that we lived just a tad above sea level.

Since moving, I have yet to find a formula for hard boiling eggs where the shell peels easily and cleanly.
I am using old eggs
I am adding salt
I start from cold water
I boil for 2 minutes and then sit for 8, then cold water and into the fridge.

The eggs themselves are fine...still bright yellow, but the membrane inside the shell, which used to be slippery and would come off the egg itself quite easily, now is inelastic and dry and often pulls bits of egg white off with it.
And, where I used to be able to separate large pieces of shell, the shell is coming off only in very small pieces.

So hit me with suggestions...but let me know if your ideas have actually worked at altitude or not.

Thanks!!!