@cas Hi cas, thanks for your help!
I didn't have a fixed 3.3v regulator so I set an adjustable LDO regulator with resistors to 3.35V. Bypass is 0.1uF multilayer ceramic cap + 1000uF 10V aluminum electrolytic, total loop length less than three inches. That seems to be good enough. (For anybody trying to use an LM317, beware the dropout voltage is too high to use a 5.2V phone charger, you need a newer regulator or a higher input voltage. For those using an AMS1117-ADJ the resistors you need are 330 and 543=33+510 ohms.) My Omega2+ came up. It took a few restarts to get it through the initial setup and firmware download, and one more after I gave it our household WPA2 passphrase. I don't use Zeroconf at home, but it was easy enough to get the Omega2+'s IP address from the router logs.
Next I need to learn how to control suspend, hibernate, and resume, and take interrupts on I/O pin transitions. Wake from suspend on an I/O pin change would be really nice. That was pretty easy on Raspberry Pi and Arduino (interrupts only), just have to find the docs.