> 127-0-0-1.backname.io resolves to 127.0.0.1

Is this enough to fool Edge (Windows 10) into allowing you to view your local Apache development environment?

That should allow access to port 80, maybe. But for TLS, you still need some CA to certify you're you. And you won't be able to convince LetsEncrypt that you control 127-0-0-1.backname.io because it resolves to localhost, which isn't you (from LetsEncrypt's perspective) :-)
:-(

Developing on a webserver that runs locally on your desktop is becoming more an more painful.

If you want a CA you can just make a CA and add it to your trusted certificates.
Not sure if this works for Windows, but the author knows what he is doing and his technique seems fairly well thought out.

https://github.com/FiloSottile/mkcert