I guess if I never wanted to have any unbalanced antennas in the future, I'd
go the balanced tuner and be done with it. But if the loss through the 238B
and DXE Tuner Balun would not be substantially greater than the Balanced
Tuner, but will permit me to match unbalanced lines too for future antennas,
then that sure seems the way to go (and adjust the feed line length to best
match).

What do you all think?

And thanks for you many replies that have brought me this far so far!

My suggestions:

Buy a used Johnson Matchbox for much less than the Palstar. Even the "low
power" Johnson will take a KW. Or if you have the $, get the Palstar.
Use it with a center-fed/ladder line dipole.

Re the inverted L: you are making it much too hard! Just put up a 160/80
inverted-L and feed it directly with coax. There is no need for a tuner
for this antenna (unless maybe you want to cover both CW and SSB on 80).
A separate 80m element can just be paralleled to the 160 wire, like a
"fan dipole". Put down lots of radials. To match the lower impedance on
160, just use a hairpin coil at the feedpoint.

Tor
N4OGW