A really good amateur project would be to combine the smart controller
of a modern auto-ATU with your own individual collection of large
inductors, capacitors and relays.

That really would be great. I'm keeping that in mind for some day.

For a non-random-wire installation and not too many bands, you can go
with manual switching of networks. When I lived in an apartment, I
had a magnet wire antenna that consisted of two random lengths fed in
the "middle." As such, every time the antenna broke and I put it back
up, I needed a new match on each band. This is the kind of a situation
where an autotuner really shines; I decided to use a remote manual
tuner instead:

http://www.n3ox.net/projects/servo

When I moved into a house, I was able to put up something a little
sturdier for the lower bands. Since it's always the same radiator
and always the same ground system, I'm just using switched L-networks
at the base to match it. It's 40 feet tall; the 80m matching network
is a 20 turn tapped coil, #10 copper wire, about 3.5 inches in
diameter. The other matching networks have air variable caps and 2"
self-supporting #10 coils.

http://www.n3ox.net/projects/lowbandvert

John, if you're thinking of using a 33 foot vertical on 160,80, and the
higher bands, might I suggest an approach where you use a GIANT tapped
coil matching scheme for 160m, taps switched with a big relay, and then
have relays to select whether you're using the 160m/80m matching
network or the autotuner. For both of these bands, an inductor with
the bottom end attached to the ground system with a tap near the bottom
for the feedline and a tap up further for the antenna should work fine.
It's basically an L-L step-up L network.

The autotuner should be fairly efficient on 40m and up, though you
might want to add a few feet to the vertical to avoid the high
impedance of a half wavelength on 20m, but I dunno.

It's really the bands where the vertical is significantly shorter than
a 1/4 wavelength where you need a high-Q matching network.

Dan