gigantic

Hear me out: Passive radiator and PEQ: flat response from 23Hz to 20Khz.

I'm currently running a pair of the new Fosi Audio ZA3 as mono blocks to drive the woofers on my horn speakers and by next week, I'll have another pair to drive the tweeters. I've been rolling op amps in them and so far, I'm deeply impressed with the SQ. There is zero noise and the separation and imaging are exquisite with MuseS02 op amps in them. Next week, I'll also get a pair of Sparkos op amps to try, and will be able to a/b them. I'd previously been using a pair of Alesis RA150 mono blocks on the woofers and an Emotiva Mini-x a100 on the tweeters; they're great amps that performed well, but after a couple weeks with the ZA3, I'll concede that the class D amps are more betterer.

the horns and PEQ settings are optimized to work with a baffle, so I suspect the results would be less than optimal.

it's worth noting that the Heritage Dealer Locator is woefully out of date. of the 7 Heritage dealers listed in my area, only 3 are open or carry home stereo gear. Of those three, only two have any Heritage product, one store has 2 pair of Forte, the other has the full Heritage line. Still, it seems they've updated it since I last checked it a couple years ago and dropped some of the out of business dealers.

There are very good Class D amps available for under $250 each. You could use inexpensive amps to drive the woofers, a nice amp for the mods and more affordable amps for the tweeters. You could capably Tri-amp for well under $1200 or less.

Not boosting it down low, but attenuating from about 60 Hz to 300 Hz? Fascinating. I'd love to see the PEQ figures on that, not that it's useful to me, I have a completely different alignment, but it is interesting just the same. There are a number of us elsewhere who are using DSP, but we're getting more extension via DJK mods and unauthorized drivers. I'm particularly curious about the phase and group delays, whether Roy is using 6dB Linkwitz-Riley filters and natural driver roll-off, steeper slopes or a quasi-linear phase alignment. That can have a profound effect on imaging and soundstage presentation. All good stuff!

interesting. I'm curious to see the Frequency/Phase and impulse responses on them. It's impressive that Roy has managed to get them down to 45Hz without porting.

Remarkable

Crites speakers sells replacement gaskets. This, is the most likely source of the distortion you're hearing. before you spend another cent, replace them.

the word you are looking for is "voila".

I've had really good results using Benjamin Moore Advance Hybrid Alkyd Acrylic enamel.

I used it for everything but the mahogany trim for the build that I detailed elsewhere. It takes about 5 days to cure, but then it is quite durable. I then clear coated it with automotive 2K poly, but it probably wasn’t absolutely necessary.

I’ve had extremely good results using Benjamin Moore Advance hybrid alkyd/latex enamel. I restored a pair of H700 Heresy decorators with it and used it on my current speakers. It’s better sprayed than brushed or rolled.

Heresy IV will run circles around Heresy I: the tweeters are far superior, the mid horn is better, as is the woofer and the crossover network is better tuned. Further, the H-4 offers better bass extension- the ported cabinets dip into the 40Hz range, compared to the mass roll-off of the H1, which is above 50Hz. That said, your Heresy 1 have a lot going for them: the cabinets are made of real wood and many prefer the K55 squawker driver to anything Klipsch has used since. There are things you can do to make them better: first and foremost, the gaskets between the mid horn and driver are dried out and are probably adding sibilance to the sound- it's super easy to replace them. Your capacitors are likely due for a refresh- even if they measure well, their ESR has probably drifted into undesirable territory. It's not difficult to replace them yourself and there are options if you don't want to break out the soldering iron. you may or may not find improvements in replacing the tweeter diaphragms, they are a known weak link in vintage heritage speakers. Lastly, your cabinets would respond well to being refinished- I've seen far worse. without delving into mods, refreshing your Heresy 1 will improve the sound, but the Heresy Four is better in nearly every conceivable way.

If your capacitors are 55 years old, they're likely due for replacement. Even if they measure correctly for capacitance, their ESR is likely well out of spec. The resonance could be due to the gasket between the K-55 and the horn- at their age, they're likely dried out, but in my experience that often expresses as sibilance and distortion, but ymmv. Definitely replace the gaskets and definitely recap your networks. It may or may not solve your resonance issues, but it will definitely improve the sound. If the resonance is coming from the horns themselves, there are ways of taming that, but I'm not sure that we're allowed to discuss those things here.