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Have you tried using the reflection and actual image of a plum line to do the adjustments?

I have tried this when levelling a mirror, as far as I can tell it works to well within 1' of arc if string is thin and straight enough.
I found that it should preferably be braided (otherwise bob will spin and wiggle line) and have a well centred attachment point (otherwise line can "lean"), personally I use ones that look like the ones used in surveying, mine weigh in at 122g and have a plastic screw in top with a hole through centre (material feels "oily" so likely PTFE or PEHD).

The trick seems to be holding string still while dialling the thing level and looking at the string such that one can see string near bob and reflected image of string close to ones hand (or like later did a 2m stick) at same time, when these are one continous straight line that side is "level" then move it so you see things 90° to original orientation (mirror should not be touched in any way) then adjust this until "level" then repeat, when string has no dicernable kink anywhere things are reasonably level.
my sextant results are well within 1' with this method after practise.

The only downside is that it is slower than using two good level vials and not as accurate as when using my 6" vials, but no real surprise there i guess...

math wise i figured that if reflection near top of line and near bob appear as one unbroken line this is at worst 0.3mm over 2m in my case (string is 0.2mm diam) and roughly 1.8m long.
taking that 0.3mm over 1.8m is just under 50" error if I made my maths right(I would say half that average).
A trick I was shown by a person passing by was to have the bob submerged in liquid (he said oil, but personally I think water is more user friendly), this dampens the efect of the wind quite a bit.
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