This is either a problem that Google is inflicting upon me, or a problem I am inflicting upon myself. I'm not totally sure.
When I first created my website a couple years ago, it followed a path similar to: http://www.mywebsite.abc123.com
Now, after a change in hosting services, I changed my domain to simply: https://www.mywebsite.com
I also added an SSL certifcate at the time for what it's worth. And it's been almost six months. I have all the variations (past and present) of my website registered and verified with Google's search console, but I can see no reason why the http://www.mywebsite.abc123.com link is getting indexed over the https://www.mywebsite.com link. I actually just assumed that http://www.mywebsite.abc123.com wouldn't even work anymore.
I've read about 301 redirects and it looks like something like that would solve my problem, but upon trying to implement it, I was confronted with nothing but a "Too many redirects" error.
Long story short, Google won't index my newer better URL.
But Yahoo and Bing will.
301 redirects have to be set up in the old domain so that it will point to the new one. If you still have access to that domain, you can add the redirects via .htaccess or in the admin panel.