i have had some experience with a hydrogen filled balloon and a longish wire. I have also seen up close, kite elevated antennas in action.
I have measured 80 m dipole voltages and currents when a thunderstorm was in the vicinity and also on dry windy days. I think I can add some practical comments.
The voltages induced by the build up of static electricity present in dry air or stray charges from nearby thunderstorms can be many 10’s of kV, but the total charge is small and hence available continuous current is 10’s of uA at most. If you get a mA then you are in a bad place at a bad time.
If you use a high ratio transformer at the end of the wire it likely has a dc path from the wire to the coax braid. If this is the situation - check with an ohm meter- then just earth the braid with a wire to a rod stuck in the ground. An earth resistance of even 100 ohms is fine. That will bleed away all the static charge quietly. No extra rf loss either.
Otherwise as has been said add a resistor of 100 k to 1 M ohm from the wire to a ground rod. Make a proper job with lugs, terminals or clips and a durable lead. This talk of losing the resistor on the mount suggests a very poor approach to a serious problem.
The resistor and ground rod need to be in place before raising the aerial unless electro-shock therapy is your thing.
Andrew you are right in that on some frequencies the resistor whether wire wound or not will appear inductive. At higher frequencies the shunt capacitance will become the main impedance contributor. I would use a common leaded component resistor. Just a few cents at your local supplier.
For field operation half a watt rating for the resistor is more than adequate.
Should you miscalculate the weather and there is a lightning stroke within a few hundred metres I suggest leaving the antenna connected and crawling away. Standing up next to such a setup invites trouble. Your life is of more value than the rig. It is possible the antenna will act as a lightning “arrestor” but it may also invite a big discharge.
Antennas elevated by these means will probably be most useful at the lower end of the HF spectrum. A conventional vertical or dipole will be more practical and more effective for 14 MHz and above for SOTA IMO. A near vertical wire that is many wavelengths long will fire most of its energy straight up. Even for wire angles down to 45 degees a wire more than a wavelength long might not radiate where you would want it to.
Some old timers used to wire a 10 k ohm half watt resistor across the feedpoint of their dipole so they could easily detect a break in the feeder. It also had the useful effect of bleeding charge on the “hot” side of the dipole to ground.
Good luck to all who go fly kites.