For a design like the Rogers/DeForest with these 50µF caps, the coil inductance should be between 5 – 20 Henrys, with wire and insulation which can easily handle the current (which I haven’t calculated) and the voltage (say 250V) supplied to the circuit. I haven’t looked at the following link, because the software mentioned is for PC only, but it may (or may not) give you the info you need, after a bit of ferreting about for current / voltage estimates:
Alternatively, you could take the very reasonable view that the issue with the existing coil is most likely to be in the flying lead connections, and you can find out, by unwinding, where the disconnection problem is. Much cheaper, and a bit more fun, than just replacement! As long as you’re prepared to walk away from the debris if it doesn’t work out – but then you’re still no worse off.