It's annoying, because the tx output Z I'm trying to match is (by a
strange coincidence) 140 ohms! So a folded dipole would be ideal, I
guess. However - and it's a big *however* - I can't use one. I'm stuck
with a telescopic whip and a ground plane the size of a box of Swan
Vestas. I imagine the radiation resistance of such a non-ideal antenna
is pretty low, but until someone can gimme a ballpark figure for it, I
can't even begin to think about how to go about matching it. :-(

Depending on frequency in use, could you do it experimentally?

The way I tune up antennas for ham bands is to hook up a mfj 249 and the
tuner to the antenna, get a best fit with the 249 and then replace the 249
with the radio and fine tune from there. There always seems to be some small
differance between the result from the mfj and the meter built into the
tuner, and at full power I would rather trust the meter built into the tuner
(a Millen transmatch jr).

You could build an L match with a tapped inductor and variable cap, then
experiment with values until you get somewhere in the ballpark of being
matched. From there it is is just small adjustments to get perfect matching.
thanks, John.
KC5DWD