Thank you for your input.
I tried to make it pretty clear that I understand about Vo, hence my comment about adding a pot if there's not a (workable) adjustment on this commercial product.
I thought it pretty clear that I understand calculating series resistors for LEDs. Yes, a 10 ohm resistor with a typical Vf of 4.2 volts is somewhat miserly for a display that would like 240mA, but the backlight should be more than faintly visible.
Both the lack of a pot and a dim display with what should be a reasonable current lead me to believe both may be firmware controlled but as I stated, I haven't found any button combination that leads to a set-up menu.
I'll know more when I trace out the board.