Thanks for the RTFM, but I have already read those.
Thankfully you were right about reinstalling with Google Play Services being installed prior to Signal. What's strange is even the things you linked say Signal has a fallback that doesn't require Google for notifications. Unfortunately, I could not register my number with Signal unless I had Google Play Services. It would ask for a captcha. When I filled it out, it would take me back to the verification screen. I'd click again to tell it to give me the text and it would say I've attempted too many times recently and give me a timeout. This happens every time and the timeout just kept increasing. Incredibly frustrating. I installed Google Play Services while Signal was already installed and this got me through verification. Afterwords I uninstalled. The way everyone makes it sound, Signal should just figure out I don't have Google Play Services and do notifications via their fallback method. Maybe something changed but that doesn't seem to be the case anymore in my experience.