Because HF signals go all around the world, this is really evil and probably violates some international law.
Cuban HF radio (radio Havana) comes in extremely strong, too strong, near new york. Its too strong, and like the bible thumpers (overcomers ministry) it seems so strong sometimes that its causing band splatter.
Those two things are high annoyances to my attempts at radiolistening.
I wonder what the voltage is at the input terminals.
Seeing Havana is about 1300 miles away from you, I don't think the splatter is created by overload to the input of your radio.
I would suggest that Radio Havana may be clipping their modulating signal hard, causing artifacts outside the allocated bandwidth of their transmission, along with audible distortion of the received programme.
The "God botherers" may be doing the same thing.
The other, probably less likely, alternative is plain old overmodulation, which sounds similar around the transmissions fundamental frequency, but would also cause the transmission of strong harmonics, which you should be able to hear on higher bands as well.