The MFJ-962C "1.5kW" Versa Tuner III description claims to contain a
4:1 current balun. I'm using that "balanced" output on my HF
almost-doublet (slightly unequal leg lengths) with fairly decent
results.

The balun only has a single core. From what I understand, these "4:1
current baluns" aren't.

Furthermore, my antenna presents both higher and lower impedances than
50 ohms depending on band.

For convenience, I'd like to have a single port that I connect my
antenna to at all times. I've remoted this tuner and I don't want to
make more complicated switching arrangements. Is it worthwhile to
rewind the "4:1 current balun" as a 1:1 choke balun?

It seems that it might be more appropriate for my application. I
should expect the core to work well for any HF transmission line
transformer I'd like to wind, as long as I don't saturate the thing,
right?

73,
Dan
N3OX