You have some impressive attempts there, I'm in awe of the rolling of the foil edges! I've had the (possibly) bright idea of using my scanner as a 1:1 scale camera. I've attached a PDF, scanned at US letter size, so if you print it you should have an actual size template. The top sector is better than the bottom one, which has had some repair (actually both have, but the bottom one more). Don't worry about the white gaps, they are reflections from adhesive rather than actual gaps.
With regard to the foil. The mass will affect the time constant rather than sensitivity - the vane is very light. Thicker foil will take up more of the gap, which might affect sensitivity. Flatness is an issue, but maybe not as much as you think. My reasoning is that for every distortion, if part of the vane is higher, it is closer to the top of the quadrant, so experiences more attraction, but further from the bottom, so experiences correspondingly less. The effect is probably not linear but reduces the importance of absolute flatness.
For the material, the lighter the better (this reduces your out of balance concern), it should end up really fragile! If foil is giving you rigidity problems, I would be tempted to try thin paper, stiffened with cyanoacrylate (which really does strengthen it) and made slightly conductive with either something like a distant spray of the Aluminium/Zinc spray sold to protect car exhausts, or possibly a light rub of powdered Aluminium or Graphite. It really doesn't need very conductive at all, the vane 'load' impedance is pretty much infinite, a bit like the diaphragm of an electrostatic speaker but under much less electrostatic stress.
It's also worth remembering that these electrometers were typically used as null detectors, comparing a very high impedance unknown voltage with low impedance reference voltage from, say, a potentiometer. The information only gives a single data point typical value (150mm deflection at 1m for 100mV, with a 100V vane bias), it doesn't define sensitivity in mV per mm. I would expect the actual readout to become non-linear fairly quickly as the vane moves more into each quadrant. There would also be non-linearity with a rotating mirror reflecting onto a flat scale. For absolute measurements (one input grounded) the user would probably calibrate their individual instrument for scale reading at specific voltages, probably plotting a curve for intermediate values. This would be easy to do using a potentiometer reference. There is no data provided for the two other filament thicknesses or the phosphor bronze one (apart from approx 1/10th of the deflection of the 0.004mm fiber).
I hope these thoughts help anyway. PDF attached.
P.S. I tried to scan an image of the assembly on its side, so that you could see the position of the mirror etc. but the vane held it too far from the scanner platen.