I do not use the dock, but I use a powerful 3.35v 2A power supply
Theoretically - especially if that is a mobil charger and probably those are not measured values.
Yes you have, especially if that is not a mobil charger and you have measured those values.
Possible solution: thicker and as short as possible power wires, a capacitor (say 22-47 uF tantal or good Al elco) at the Omega's power input pins and good connections at those pins.
PS. you said
Omega2 does not boot from a USB-to-TTL adapter
That adapter provides a serial connection / serial terminal only.
Omega - when no reset button pressed - does boot from an on board flash memory chip.