Man, dealing with a traditional radio for these kinds of signals feels like wearing sunglasses at night, a waterfall display tells you so much more.
Assuming it is not a local signal or RFI:
This appears to be a pulsed signal (a waterfall would make that more clear). As you said there does not appear to be a hetrodyne when you go to SSB and tune across the signal, and while the pitch of the heard signal changes as you tune across it in SSB, the spacing of the harmonics of the pitch do not, the combination of these features strongly suggest pulsed. A strong case for pulsed, but not certain. The tone heard in AM mode (and the harmonic spacing in SSB mode) is the "PRI line" of the pulsed signal, in this case 325 Hz.
Most often such strong pulsed signals on HF are either radars or ionopsheric heaters/experiments (such as Arecibo or HAARP). There can, of course, be other explanations.
In other words, we ain't gonna know from this recording alone.
Is it a radar? Could be. The PRI (Pulse Repetition Interval) used is very close to what is used by several radars, including the Russian Sunflower radar. However, I doubt it would be the Sunflower specifically, as I don't think that is ever heard with that big a signal level on this side of the Atlantic.
Could it be a heater of some kind? Could be. However HAARP is not currently active on a campaign, and while Arecibo is active, the HF components of their testing were not scheduled at that time (the last scheduled HF work before your reported time was at 1300 UTC on May 16, 2019, if they are holding to their published sched) and Arecibo was scheduled to be in the 8 MHz area. So if it was a heater it was probably not one of the two big ones in the region.
At this point, with the supplied data, it is easier to say what it is not, rather than what it is. But I would not rule out a BC transmitter test that involves pulses instead of AM audio.
If you hear it again you may want to try and TDOA it on the Kiwi network, that will give you the location and that could narrow things down a bit.
T!