"I know only a handful of states offer amended tax return e-file compatibility"

Well, I did more research for you, as you asked.

Other Software handles more than a handful:

https://support.taxslayerpro.com/hc/en-us/articles/360009294893-Electronically-Filing-Amended-State-...

https://www.taxact.com/support/936/2016/e-filing-amended-state-return?hideLayout=False

Those were my first two web search results.

Hope that helps.