My experience with an EFHW is not quite what is here being described. A wire that is resonant on 40M wasn’t resonant on any of the other bands without some adjustment. I think the reason why is what is known as “end effect.” The wire is two halfwaves on 20M which would want four ends to be “right on” but there are only two.
I got a 40M EFHW to be exactly resonant on 20M by dropping a short stub from the middle of the wire. This stub was about 18 inches in length. It is ignored on 40M, and its length can be adjusted for perfect resonance.
Incidentally,the wire can be deployed in a shape called a half square which leads to a 40M dipole behavior, and a two element bi-direction vertical beam on 20M. While not perfectly resonant on 15M, it IS perfectly resonant on 12M, and with a little help from a tuner, will be usable on 15M.
You can certainly shorten an EFHW by placing an inductance coil at the end of the higher band’s half-wave length and thus choking this off and acting as a loading coil for the lower band above it (which will of course be shorter). I have used and designed many of these as dual band antennas and there is the much used three band (402010m) version using a 33uH coil too - this will be around 11.8m in length.
This appears to refer to winding 1/2 wavelength of wire around a 4cm diameter pipe to make a shorter helical antenna, with the thought that it would still have the same resonances as the same length of straight wire.
The problem with this line of thinking is that the required wire length is not a constant when winding it into a coil.
For example, when building a helical 1/4 wave vertical for 160m, the ARRL Antenna Book suggests that it requires 1/2 wavelength of wire to achieve 1/4 wave resonance (with a capacity hat of some sort of capacity hat at the top to prevent corona effects). But even that is for a particular antenna length, diameter, and winding pitch. An Australian source used 3/4 of wire in a tapered winding to make a 40m mobile antenna on a fiberglass fishing rod, claiming that, with an appropriate variation in winding pitch it could be made to resonate on 20m, 15m and 10m as well. One of the helical wound CB whips used to advertise itself as a “5/8 wave antenna”, because that was how much wire wound onto a 1.5 to 2m rod for quarter wave resonance at 27 MHz. (Of course, it doesn’t perform like a 5/8 wave antenna!)
Those examples should at least give a sense that it isn’t merely the length of wire used that determines the resonant frequency of such an antenna. And the effect will be different on different bands.
That’s not to say that it is impossible to get such an antenna to work, just that it is rather more complex than it might seem initially.
I think a helically loaded antenna should work; that’s how your rubber duck, hamstick, slinky antenna, etc. look. But what does your MMANA model say about the pattern? A 20m vertical wire models as pretty poor pattern on 15m and 10m, sending a lot of power into space (or at best short hops) due to the opposed half-waves close together in line (I think). I would guess that helical loading that puts the opposed half-waves closer together in absolute space would make this worse.