the current drain will still be very similar,
I guess the remaining opinion I hold is that it is possible that there is a driver on board the LCD
according to the attached data sheet it should be out of regulation
Plus, out of regulation doesn't mean it doesn't pass power anymore. It just that its ability to regulate output voltage is gone.
The reality is that you have a very high gain DC amplifier with an unstable reference voltage.
a more understandable comparison might well be that you have a really big car (The Regulator) moving across an area (output Voltage) without a driver (The Reference Voltage) High gain because the reference term is a current (Typ 100uA) controlling a regulator capable of an Ampere of current and it doesn't take a genius to figure out that 100 uA is a tenth of a milliamp and as the name implies a milliamp is 1/1000th of an ampere so we have a gain of 10 X 1000 and no stable input reference. The typical result for an NPN pass type (AKA 78XX series) is oscillation and for the PNP Pass types like the AMS1117 the reference term is a part of the load current... So there is a minimum current that must be drawn from the regulator for the regulator to be stable and a processor unfortunately doesn't fit that condition... again the result is typically oscillation.
Now what can that mean? What kind of POWER DOES IT PASS
My intent here is to point out that
Let me be the first one to say that I have absolutely no clue what the above is talking about and I doubt you do.
To give you some sense, I have a board with the following load: 3 avrs, 1 pic, 1 1602 lcd, two hc132 oscillator (14Mhz + 70k), two hc04 oscillators (4Mhz + 12Mhz), 1 4-digit 7-segment led, 1 25Mhz oscillator, 1 14.7Mhz oscillator, one rgb led, 9 bright leds, 2 7-segment leds.Powered from a 15v Verizon phone adapter, regulated down to 3.3v, the linear regulator (to220, no heatsink) is lukewarm. I think I measured my current consumption at one time and it was around 50ma.
I made my first discrete 40 years ago...
Might have to get one of those well regulated USB charger supplies, I've run out of suitable wall warts to test.