Indeed, I never did see Ben Eater's schematics, just the video. Now that I saw he added a capacitor in there, I just put that in my own circuit to test it. Attached is a picture of what I'm using right now (the IC used here is the MCP130xxxD, could also be a DS1813).
I don't know if that capacitor is hurting a lot or not, but it works on power up and push button WITH the MCP130 attached.
I then removed the MCP130 and it STILL worked, both on power up and push button.
I'm using a 10K pull-up, but Ben Eater is using a 1K pull-up. That's the only difference. And so far, with my minimal testing, it seems to work fine enough. I reconnected my MCP130 anyways because I'd rather be extra safe, and I want to test it like for the next few days. I can always clip off the capacitor and resistor if I wanted to.
This doesn't prove that a 10K pull-up with a 0.1uF cap is truly good for power on reset. But at least it works here, on this board, at the moment, for right now, at least a couple of times in a row. Lot's of stipulations
Thanks everyone.
Chad