The maximum voltage you can use is 5.2v anything above that could damage the Pi.
I’ve measured mine this morning on the Pi GPIO and it shows on average 4.85v with the volume at maximum. I also tried playing Mario Kart on the Nintendo 64 and there was no change. The undervoltage indicator never shows on my system with this voltage. During boot it dropped to 4.78v which is still above the undervolt threshold at 4.65v.
The problem with using a multimeter is they tend to display an average so its difficult to determine the lowest value without using an Oscilloscope.
The USB cable I use for the Pi to Picade board is the one supplied by Pimoroni. It does seem strange that you are experiencing these issues as I am also running the screen from the same converter that is powering the Pi. Mine is setup up as
PSU -> Converter -> ATXRasPi -> Pi
Did you solder the USB connector on the output of the ATXRasPi if so just check you have no dry joints here.