Jack,
Yep, lots of fun with the up/down/up/down thing, but that's
just the normal part of tuning almost any antenna I can think
of, off hand. For a multiband antenna, multiply all that up
and down stuff for each band (probably). And since each 'part'
of the antenna will affect the other 'parts', repeating the
whole mess is something to count on till all of them are
'right'.
One way of changing the input impedance of a dipole is to
change the 'angle of the dangle' of each 'element'. Making the
angle between the legs of a dipole smaller reduces the input
impedance. So playing with the 'dangle angle' of each part of
the multiband antenna can be one of the simpler ways of doing
the impedance matching. Something to remember is that the
input impedance for all bands will probably never be 'perfect'.
Settling for the 'best' you can get is probably what the
majority
of people do, and just don't worry about it too much. While
looking for the 'best' you can get is the idea, working for
'perfection' is usually a wasted effort.
The thing about using an electrical 1/2 wave feed line is
mostly
for tuning purposes. Once the antenna is tuned correctly the
length
of feed line (coax type) isn't very important, since it isn't
being
used to do any of the impedance matching (right?).
I don't remember what else you mentioned in your post. It's
late,
I just got off work...
'Doc