An important correction: I DO NOT get a lower-than-50ohm *impedance* on
any band.

I may be taxing the limits of my '259B but this is what I measure as
far as ballpark magnitude of impedance.

80M 225 ohms
60m 600 ohms
40m 630 ohms
30m 330 ohms
20m 420 ohms
17m 206 ohms
15m 216 ohms
12m 216 ohms
10m 180 ohms

Nowhere is this resistive.

So, maybe the 4:1 current balun is the more appropriate one. How does
the impedance transformation work with reactive loads?

Here are the impedances if anyone needs:
80m 41-j220
60m 500-j320
40m 500+j370 when paralleled with a 1k resistor (300+j1000ish?)
30m 39-j325
20m 300+j255
17m 50-j200
15m 190+j104
12m 70-j205
10m 170+j60

Will a 4:1 current balun transform a random impedance Z1 to Z2 where
|Z2|=|Z1|/4? I know Roy pointed out that this won't work for a voltage
balun...

73,
Dan