Rick wrote:
Doesn't the horizontal part of the inverted L need to be as high as
possible for best results? I'd run into the same problems I'm running
into in putting a dipole or inverted V up high enough.

Not exactly. Make the vertical section of the Inv-L
as long as feasible. The vertical section is the
highest current section and therefore has the greatest
effect. Or instead of an Inv-L, make it a T antenna
with a vertical section and a symmetrical top hat.
The symmetrical top hat doesn't do much radiating.

Here's what EZNEC says using VERT1.ez as the reference.
40m 33' Vert1 has -0.04 dBi gain omnidirectional.

16.5'-16.5'Inv-L has 1.04 dBi gain with some directivity.

16.5'-23.5' T antenna has 0.19 dBi gain omnidirectional.
Note: 16.5' = vertical, 23.5' = horizontal top hat.

Performance wise, I don't think you could tell the real
vertical from the T except for the T's lower feedpoint
impedance.
--
73, Cecil, http://www.qsl.net/w5dxp