Here's the thing that I've yet to comprehend about a G5RV. The antenna is intentionally non-resonant so that most tuners can handle the mismatch on any amateur band.

Well, not exactly. Actually it is designed to be 3/2 wavelengths on 20m, a resonant length

that gives a 6-lobed pattern that was well suited for a lot of DX directions from G5RV's location.

The half wavelength feedline, while operating at a moderate SWR, repeats the ~100 ohm impedance

of the antenna feedpoint at the bottom where it connects to coax. This gives a relatively low SWR

on the coax (especially when using 75 ohm line, or the 72 ohm twinlead that was more common back

in the 1950's than it is now.)

That particular combination also presents a usable SWR on 40m, the bottom of 80m, and on 12m,

so coax losses are relatively low on those bands. On other bands the SWR on the coax is higher,

so losses will increase (even if your tuner can match the impedance.)

...I must argue that the length of coax fed to the balun on a G5RV matters just as much as the length of window line up to the antenna...

This is true with regards to the impedance seen at the tuner end of the coax, but the length of the

window line determines the actual SWR on the coax, and that affects the range of impedances that

can appear at the tuner. For example, finding a combination that gives an SWR of 2 : 1 on the coax

limits the impedance the tuner has to match to between 25 and 100 ohms (likely with some reactance),

consistent with the SWR of 2 : 1. If a different length of window line, or operation on a different band,

causes an SWR of 10 : 1, then the corresponding limits are 5 ohms to 500 ohms instead. The former is

within the matching range of many built-in autotuners, while the second may not be.

You see, if there is a mismatch on the balanced conductor, there will be a mismatch on the coax.

This is NOT true, and it is an important factor in how many antenna matching systems work.

For example, imagine a dipole with an impedance of 50 ohms fed through an electrical half

wavelength of 600 ohm open wire line. The SWR on the open wire line is 12 : 1, but because

it is a half wavelength long the impedance at the bottom end is the same as at the top,

namely 50 ohms. So there is a high SWR on the open wire line, but 1 : 1 on the coax

connected to it.

In fact, that's how you operate your antenna system without needing a tuner: how do you

think you are presenting a 50 ohm impedance to the balun on each band by changing the

length of the feedline if the window line is not operating at a high SWR? If it shows 50 ohms

to the balun, then the SWR on that line must be 450 / 50 = 9 : 1.

To get back to the OP, there are several types of antennas that will allow you to operate

multiple bands. One is to add dipoles for different bands to feedpoint of your current dipole:

I often use 80m, 40m and 20m dipoles strung out in different directions from the same

feedpoint (and the 40m dipole works well enough on 15m). The "doublet" that several

others have mentioned is simply a dipole of non-critical length fed with ladder line to a

tuner in the shack: the ladder line is capable of operation at high SWR with lower loss

than coax, making it less lossy for multiband operation.