Can I amend the last 3 years of returns to take depreciation on a rental house that I have overlooked for 11 years or do I have to change the accounting method?

Yes, go ahead and amend your prior year returns.  You should bring the depreciation amount up to date, meaning you need to calculate depreciation from when you should have started taking it which was back in 2011.  Then each year thereafter, a fixed amount of depreciation is taken against the 2011 adjusted basis of the rental or the fair market value whichever was less.  Here is an informative TurboTax article that addresses your tax situation.

What should I do if I didn’t take depreciation on my rental property?

I disagree since the error goes back more than 2 years

see this link

https://www.msatp.org/fixing-the-error-how-do-we-solve-depreciation-mistakes/#:~:text=Once%20an%20incorrect%20accounting%20method%20has%20been%20used,a%20Change%20in%20Method%