Wawa:
I understand from the datasheets of the chip and the Kingbright display that the IC's supply voltage has to be exactly 10volt (regulated).
Leo you need to learn how to read data sheets. Page 4 at the top left in bold print it says:-
Supply voltage (VDD – VSS).......................... +4.75V to +11V
And that the LED current (brighness) is 20x the current into pin 19.
Yes.
And that that current has to come from the 10volt supply.
No
I would try an opto coupler.
Opto LED driven via 1k current limiting resistor from a PWM pin.
Opto transistor and a 100k trimpot in series between pin 19 and 20 of the LED driver.
Set the trimpot to max LED current (20mA).
No.