I received my order of MCP1755 voltage regulators Friday and soldered one of those tiny SOT23-5 devices on to an almost equally small breakout board.
I used it to power a breadboard version of the clock controller. Seems to work ok. I had some strange resets on the ESP8266, they are very sensitive to their power being stable, but they seem reduced after increasing the output capacitor.
Power fail testing shows using the power good output from the MCP1755 works much better that using the reset output from the DS3231. Additionally, the 510uf capacitor provides more than enough juice to manage a tick and save the clock position information with room to spare.