Adding what I like to call "magic capacitors" to antenna systems is non-productive, and sometimes downright deceptive. If you want to move the resonant frequency of your 80m EFHW up, then just shorten the wire.
The same holds true with the unknown capacitance of using a bifilar primary winding, or adding a capacitor across the primary to get a deceptively low SWR on 20 or 10m. As with any LC resonance, you’re introducing a frequency-specific item. Many commercial sellers (and even the tutorials on the internet) advertise this as a "feature". It’s not. Your 80m EFHW is not a good radiator @ 10 meters. Period. You’re seeing a good match, not good performance.
Same with cores. At lower frequencies the cores can experience higher losses due to increased hysteresis and eddy currents. The reactance of the windings is lower and you need high-permeability cores. Cores that work good at 80/160 don't work good at 20m. At 20m the cores suffer from skin effect and increased resistive losses, stray capacitance and leakage inductance. So you actually need a different core mix for 80 than you need for 20, and saying one core fits all is another compromise. What you really need is two different antennas and transformers.
So the 80m EFHW, advertised as an "all-band" antenna gets a bad rap as a "compromise antenna" due to transformer losses, which it really is, but it doesn't have to be be that way. All you have to do is reach the realization that it's only really good on one band, and that building wide-band transformers is a bad idea from the word "go". And, unfortunately, on the one band that it's really good on, most hams don't have the resources to get the antenna high enough off the ground.
Oh yeah, some people like Danny Horvat have had great success selling these things for ridiculous prices to unsuspecting hams, even some who should know better, but it still doesn't make the misconceived concept of an "all-band" antenna valid. I realize some hams don't have the room or resources to put up different antennas for the different bands, and they are probably the primary buyers of these things. As long as you realize that there's inherent limitations to trying to cover 27,000 KHz of radio spectrum with one piece of wire, all is fine.