..Made some progress here. Step by step:
-- Disconnected ESC, connected it to a separate receiver with nothing else connected to the Rx, provided battery power to the ESC via the same 4S Lipo as always, and used Tx stick programming to reset the ESC back to all default values, which include standard 5V BEC output. (All other ESC parameters were already set to defaults.) Measured with a DVM... 5.20 volts steady. Previously, it was 6.02 volts steady.
-- Reconnected ESC to Revo Mini, then connected Revo Mini to LP via USB. Did NOT reconnect Lipo.
-- Went back into LP/System/HW Settings/WS2812 and set it to Servo Output 1, made no other changes at all, Saved the new settings, and disconnected from USB.
-- Disconnected the pitch servo from Servo output 1, connected the 6-LED strip instead.
-- Turned Tx back on, powered up the heli and Revo Mini using Lipo only, no USB connection to LP.
-- AND: it's working. All 6 LEDs started flashing single white blinks. Servos responded to Tx as before. Flipped the Arm switch, flash pattern changed to green. Flipped the Flight Mode switch, green flash patterns changed to properly indicate each of the 3 Modes.
-- Reconnected to LP via USB... no change, flash patterns still responded to Tx switch changes.
...All this leads me to one conclusion, and one question:
-- For my specific setup (simple Trex450 DFC Heli, no accessories other than LEDs, LP 16.09), and a Revo Mini from Hyperion, the problem was in fact due to BEC output voltage levels. It may be that my specific Revo Mini doesn't handle 6V well... I have another Revo Mini (never used) that I'll test this weekend, and see what THAT one does.
-- The only remaining anomaly is that the Wiki 'HowTo' section for LEDs says I should be getting blue flashes instead of green, but the flash patterns do match the HowTo. Should that be a concern?
Next step is to figure out how to shift all my heli output channels up by 1 so that I can keep the LEDs connected to Servo Output 1 (seems to be the only acceptable LED port on the Mini).