Holy crap my printer is working!
I'll get back with you in a moment.
EDIT - Pin19 is a ground for voltage feedback. It's pin20 -and- pin23 that make up the gpu's v+ voltage feedback. The way they show it is a resistor from pin20 to FBRTN(Pin19/gpu-ground) to adjust the voltage. So pulling pin20 lower WILL increase v+ to the gpu. You can also pull pin23 lower but I believe this will have a greater effect the droop control. Good or bad? I don't know. You might get too much droop control. There's an ntc parallel with r92(shown) which lowers the sensed voltage as heat rises. The regulator must then compensate by raising the voltage. Adjusting pin23 is before the droop circuit. Both pin20 and 23 -will- raise voltage but I'd start with pin20 and see how stable the voltage is with varying temps. You may find it more stable to use pin23 but they don't show that as the 'official' means of voltage control.
Messing with FB/FBRTN will probably get us with this ST VoltReg or some of output mosfets release their soul, while Vsense is used for load voltage regulation feedback afaik.
EDIT: All above will destroy circutry and it's not to be messed up outside testing this PWM chip for application purposes. VID1 (7) is probably hot pin while VID0 (8) is used to internally switch latches. So we require software voltage regulation. And manual power play is on R1-R3 pins (10-12) (only 4 states) and actual boost current source (where we mess up) IREF (9) ...... Internally Iref pin is fixed to 1.240V. So we need some load (resistor) between pin 9 and GND if we wanna go up for 1,35V we need add externally 1,1kOhm and for 1,50V 2,6kOhm. So probably theres 1k1 1/20W SMD resistor somwere on board soldered to Iref (9) to reach default 1,350V needed for HD5770.
So with 2k2 fixed resistor (instead soldered default) and some 10k pot in parallel we could regulate voltage between 1,24V-1,46V. For higher voltages change 2k2 with some higher one 100Ohm == 0,01V
Anyway this should work, it's on you're own responsibility ofc. And its poor thing that probably ATi us ST instead volterra VRM so their retailer could release SoftMod tools to HD5800 cards thru different BIOS and voltage regulation approach which wont work on budget cards like HD5770