Could such a scheme achieve low-loss, balanced tuning of the dipole (at least, within a single band) using only a single variable capacitor?
Maybe... You still have the problem that the capacitor is at a point of maximum current
in the antenna, and loss considerations are similar to when they are used in small loops.
A split-stator capacitor eliminated losses in wiper contacts, but requires twice the plate
area for the same amount of capacitance. This might not be an issue on 20m and higher.
So you could wind the normal loading coil, except break the wire in the middle and bring
the ends out to the variable capacitor. By adjusting the turns and coupling on the link
coil you should be able to get a match.
I think the article overstates the efficiency difference between the losses in a link-coupled
tuner (traditionally used with high impedance open wire line) and a T-network tuner
(often used with low impedance coax): most of the difference is in the impedance they
need to match rather than the circuit itself, and link coupled tuners (including the famed
Johnson Matchbox) have a more limited matching range. Even open wire loss can have
higher losses than one might expect when used with low impedance loads. (And expecially
the types with stranded Copperweld conductors when used on 80m and 160m.)
If this would work, is it correct that the series-fed variant (figure 3) is better (higher efficiency) for a short, end-loaded dipole with capacity hats?
You would certainly want series tuning (used for low impedance loads) rather than parallel
tuning (high impedance). And I wouldn't use variable coils (especially those with shorted
turns) if you can help it to reduce contact losses.
That said, I don't know that the efficiency will be necessarily better or worse that other
possible matching methods: that depends on the choice of components, assembly, etc.
An alternate tuning method you might consider is to make a "tuning slug" with some
powdered iron toroid cores and move it mechanically relative to the loading coil. That
may give you enough tuning range with relatively low losses while avoiding any sliding