After doing a lot of reading on the web about long wires, short wires,
inverted L's, impedance matching, baluns, ununs, onions, fundip, and who
knows what else...

I was thinking (run for cover please)

Couldn't one simply use a small active device to buffer the straight wire
antenna at the end where it tethers to Ye Olde Oak tree or whatever it's
tied to? I was thinking you could even make it powered with a small gel
cell or something and a solar cell to power it. Some sort of wide-band
amplifier that would have a suitably high input impedance to accomodate the
higher and varying impedance of the wire over the desired frequency range,
and yet having a fixed 75 or 50 ohm output impedance to drive the coax that
runs back to the house. Then you could use a transformer in the house at
the receiver if it's the type that wants to be fed from a high-impedance. I
would think this would get around the problem of an impedance matching
transformer mismatching the antenna on frequncies where the antenna
impedance drops significantly. Also it could provide perhaps some minimal
gain to boot. Some of those commercial impedance matching transformers sell
for over $50 US. So I would think a small buffer amp might not be too
cost-ineffective.

Dave