It just struck me that even the "supposedly best" verticals (5/8 wl,
using good connections to the metal roof as a counterpoise) are
consistently substantially weaker on reception on 40-10m than the
inv-V. The difference varies from zero to 7-8 S-units. I would have
expected the vertical to be better in at least a few cases - but it's
not. .......................................

The *best* 5/8 wave antennas would not use a roof
as the ground plane. I think this is half the problem.
You are running an elevated vertical, "ground plane",
but your radial system is not resonant. This would
greatly effect the performance of most all the various
length radiators. Then you have to consider the construction
of the roof, how well each piece is electrically connected,
etc, etc..Then you mention the poor overall ground rating
for your local in general. This all combines for a mediocre
antenna. Then on top of that, you have to consider the height
above ground in wavelengths, for each particular band, and
the efficiency for each band. Naturally, the lower bands
would see the most ground losses, from the low height.
I can see a 5/8 antenna for 10m being fairly poor, when
mounted on a untuned roof. In a case like that, you should
use an elevated antenna, with elevated radials above the roof.
Or, use a 1/2 wave which requires no radials. On the lower
bands, I think the performance is probably not so good, due
to the ground system not being near as good as you think it is.
Being elevated, it really should be resonant for each band to
be used. I can see it being a toss on 20m up, but on 40m, and
lower, the vertical should be best for dx. "over 1500 miles"
If it's not, it's not working as well as it could. MK