So far one of my favorite saltwater path groundwave stories is this one.
http://www.hard-core-dx.com/archive/irca/msg46025.html
Chris, While still in the employ of Uncle Sam I visited Signal Hill in St. Johns, NF in September 1988, at the peak of Solar Cycle 22. At the time I was an SWL, not yet licensed as a Ham, which came in December 1989. I had with me a Sony ICF-6500W receiver and at daytime on ground wave I was able to clearly copy WQAM 560 kc 5 kw in Miami, FL. At the time WQAM's single tower was out in Biscayne Bay. That was an approximate distance of 2158 km, 3474 mi. Part of the ground wave path in NF was over land but the signal probably skewed along and around the coast to Signal Hill.
(There is an error in the distances and km vs mi, but I went ahead and pasted the quote exactly.)
So if 5 kW into a standard 1/4-wave antenna on 560 with an ICF- 6500W would do that, I wonder what multiple dedicated 2 MW transmitters into each element of an array of
anti-fading multi-segmented (like typical FM bays)
Franklin antennas on 153 kHz would do with a good communications receiver and a quad-gang-air-core-capacitor-pretuned beverage antenna? Also what would be the radiation efficiency of such setup be for 1kW at 1km? could 1000, or even 2000, 3200, 4000 or 5000+ mV/m @ 1 km for 1 kW be achieved?
BTW I'm assuming that "clearly copy" means there was *NO* static detectable - if you cranked up the volume till your ears hurt when listening to a program, then switched off the radio during a period of non-modulation, there'd be no discernable difference in noise level. (This assumes you're listening on custom-made in-ear monitor headphones in an anechoic chamber.)
As for how loud I mean ... I was just now remembering an incident on my bike with a flat tire. I stopped at a gas station to pump up a leaky tube so I could either get home or get to a bike shop to repair it, I don't remember which. (BTW I was listening to my radio with (I thought) fairly decent (for the sub-$20-$40 price) sound-isolating headphones.) Apparently I either put too much air in too fast, the tube was weak already, or both, cause I heard a loud bang THROUGH the isolating headphones! For the next day or two my ear on that side was ringing like crazy, and I had temporarily lost, I'm guessing, a few decades of dB of hearing around the 1-6 kHz range or so. It was something like at least a few weeks to a couple months later before my hearing had fully recovered, IIRC.
Also I'm assuming that the type of communications receiver I have in mind is sensitive enough so that with *NO* antenna at all, it gets that quality signal on a station that the GE Superradio, CCRadio2, Sangean PR-D5, etc, couldn't even detect carriers if they had QRSS CW or SSB capability.

Also the beverage antenna should have high enough broadband gain to raise a signal from undetectable to overloading as severely as
this video demonstrates. (That is, if it was just your typical Sony, Sangean, GE, Rat Shack, Tecsun portables, although the high-end comm RX should handle it perfectly fine.) Tuning the antenna should further increase the on-frequency gain by the same number of dB or more.

(I'd like to go so far as to say the comm RX should have good enough selectivity to bring in a threshold-of-detectability-WITH-antenna split-channel station just a couple kHz from an IBOC pest that overloads with NO antenna like the video, with NO splatter, but I'm starting to be dreaming just a bit much, at least for under $200 or so.)
Being maybe a little more realistic, though, how much of a difference in sensitivity can you have on radio circuts without factoring in antenna gain?