It may be thin power cables (in this case the splitter cable from single PSU) causing a small voltage drop - not a current issue, which explains my experience with a 1.1amp PSU:
https://www.raspberrypi.org/forums/viewtopic.php?f=63&t=159679
But it was the same splitter cable used with PiCorePlayer so it’s a bit strange, which makes me think Ropieee perhaps uses more power, especially on boot-up, as per earlier observations too.
I’ll try a thicker wire splitter cable.
The screen only uses ~650mA at 5V which explains why 1.1amp was enough to power Pi3 + Screen + HiFiBerry HAT with PiCorePlayer
https://www.raspberrypi.org/forums/viewtopic.php?f=108&t=128234&p=857722#p857722