You need a data line type choke, one made with twisted or parallel pair, something like that. The side-by-side coil kinds are almost as much leakage inductance, and will unmatch the tank quickly. Shop for an impedance of at least several kohms at Fo.
There appears to be a lot of mysticism about this antenna in the cluster of links on the page; to be clear, it is an absolutely, positively standard electrically-short dipole with built-in antenna tuner (fixed for the band of interest, which fortunately is quite narrow; they're only working the HAM bands I take it). The connection to that dipole seems a bit peculiar, making it at the end (where the choke is) rather than in the middle with a balun -- for which you will get exactly the same results, with a much smaller choke (or a balun proper). The difference is, making the connection at the end, the choke must withstand the full resonant voltage of the element, a big ask and likely not achieved by the toroid shown (which is probably around 2kohms at driven frequency, and about equal parts reactance and resistance; the equivalent circuit is this in parallel with the small capacitance of the elements, plus whatever else is on the cable; I would recommend a ground connection below the choke, to keep whatever line current is left, away from the transceiver).
As an electrically-short antenna, operation is equivalent to a magnetic loop of the same dimension, if that's any help.
Tim