Update for everyone:
I got it working by just pulling CH_PD high and GPIO15 low. Like I said, it's frustrating, because there are 100 articles out there and they all claim different pin combinations will cause it to 'boot normally'.
I originally hooked it up the way the guide (posted above) said, which was CH_PD high, RST high, and GPIO15 low, and that did cause it to successfully boot. But, further testing revealed that leaving RST disconnected still resulted in a good boot (RST pulled low did not work).
This test was with an ESP-12F - tomorrow I get a new set of ESP-12S's in and I'm going to test those to see if they boot different (I think they do, because my previous PCB projected booted fine with 12S's without touching 15 or CH_PD).
Thanks again!