It seems to me that, if one wanted to make a choke BalUn that covered
a wide frequency range, it could be made with several grades of
ferrite in the stack of cores on the coax, a la W2DU, with the highest
frequency material at the antenna end.

Digikey sells 3 grades of ferrite made by Steward, in long form beads
that are intended for common mode choke applications. The low
frequency material is similar to Fair-Rite type 75 (u about 5000).
The medium frequency material is similar to type 43 (u about 800).
And the high frequency material is similar to type 61, only higher
loss (u about 125).

I have long beads in all of these materials, and some more on back
order. If someone would volunteer to measure the common mode
impedance of each a set of, say, 3 of each type strung on a foot of
wire, to find the useful frequency range, I would be happy to lend
them the set of cores.