Well, too bad you did not get help from Amazon. You probably got 1st tier help. If you need to call back, next time ask for the 2nd tier of help.
Secondly, I told you the security settings for today's modern routers. I only told you because you has changed the settings to not the current recommendations. It has nothing to do with the Echo issue per se, I just wanted you to have the router set correctly for all situations. Return your router to WPA2 and AES and never change it, because it it the highest security settings today. I sent you the Apple link so you would not think I was making this stuff up!
I also seem to recall when I set up my Echo and later, a Dot, I had some connection issues, too. Perhaps once you connect to amazonXXX and the Echo tells you to go back to your phone, you may need to disconnect from amazonXXX and get your phone back on your home wi-fi again. I just can't remember the sequence (it may be after you have told the setup which signal to connect to). At any rate,it gets a bit tricky, so pay attention to when it tells you to get back on your home wi-fi. I also seem to remember that at the last step it did not tell me I was all connected -- but i was, and discovered I was after I turned Echo off and back on and Echo said Hello.
I know it can be frustrating, so maybe telling you about these two gotchas might help.. It did take longer and a few tries to connect the first time, and when I did it subsequent times it all went smoother and without a hitch.
And if all else fails, call Amazon back, and do NOT turn off your router; tell them why and that you rebooted it right before you called them. Good luck.