The problem is most people making their own version are using the wrong ferrite mix and that can heat the core up more and also provide too much inductance on the higher bands. Most designs I've seen call for a #43 mix and a single 2.4" core of 43 might only be good on 160 through 40m. If you stack cores it compounds the problem and you have to choose a still lower permeability ferrite.
Companies like MyAntennas know the best formula and their standard models that have what I believe is two cores handle 1kW SSB and 250W continuous. Their 3 core versions handle 2kW SSB and about 350W continuous. If you make one with different ferrite material you may not get the same power or frequency ratings.
I mentioned before there is no appreciable RF on the coax within their resonant bands and if you light one of these up too far out of band they will put a lot of RF on the coax. I've made a lot of these antennas, probably two dozen or more in sizes ranging from about 100W SSB to 2kW, so I have many years of experience and its all been very good. For my permanent full legal limit installs I'll use a commercially made MyAntennas but for lower power my home made versions are very popular with the local hams and they constantly praise them for their ease of deployment and also the performance.
I had a few chats with Danny that owns MyAntennas and he commented about some online posts where people who have never even used a EFHW are giving all the reasons why it can't work. He just laughs all the way to the bank with probably 10s of thousands of these sold so far with no problems to speak of. I know you have made at least one and you might consider any problems you may have might be from the ferrite mix or the way its wound. Early on I opened up a MyAntennas transformer and saw the way they treat the turns and spacing and copied that. Its a little different that what you might find online and little things like this can skew VSWR and performance.
Edit:
I'll add just a little more to this post and say I have tested a 40m EFHW against a resonant center fed dipole in the exact same location and height and there was no perceivable difference in signal level to anyone. For an 80m version there is very little difference in performance or radiation pattern compared to the same 133ft of wire fed in the center with ladder line to a balanced tuner. Sure there might be a fraction of a dB loss in the transformer or maybe up to 1dB overall loss on some higher band, otherwise exciting 133ft of wire in the center or the end gives you the same basic results and you would have a slight amount of loss in a center fed setup in the tuner.
I tried that design many years ago using a 49:1 Un-Un transformer, and a ferrite choke to keep RF out of the shack. Except in the cases where the antenna is almost exactly 1/2 wavelength, RF current will appear on the coax shield, hence the choke. My experience has been that the 49:1 and 64:1 transformers only provide a 1.5 to one or less match in a very narrow range of frequencies, this became more pronounced as I moved to higher multiples ( I was using an 80 meter half wave at 3.6 MHZ). I tested it using a network analyzer and sure enough, the transformer loaded the heck out of it.
So don't take my word for it, run 500 watts on CW or SSB for about a minute, then go out and touch the transformer (Un-Un). It will be hotter than hocky sticks because that is where most of the RF power is being dissapated. The antenna will radiate the rest minus the additional losses in the coax and earth losses. Sorry I can't be more help to you.
