My question is - based on the information we have at present - are either of these the most likely explanation, or is it more likely this is referring to a different flood event to these two?
Observations on the Genesis flood
The Zanclean flood
The immediate problem with the Zanclean flood event (which is the theoretical filling of the Mediterranean from the Atlantic Ocean via the Strait of Gibraltar) is that it would have occurred 5.33 million years ago. While that's well outside of the reach of our historical record, it also is well outside of the possibility of a continuous oral tradition. Despite some intriguing similarities to observations 2 and 3 above, there just is no way to reconcile this event to #1.
The Black Sea deluge
Having a possible date circa 5600 BC, the Black Sea deluge theory would better fit the timeframe Genesis implies. It also fits the magnitude of devastation if the catastrophic hypothesis is correct. (The gradual and oscillating models would not fit the intensity required by the Genesis account.) However, the location of the flood would be near the edge of the Levant region. Perhaps it is reflected in Greco-Roman flood myths, but given that it would have occurred 4,400 years before the Trojan War that seems a stretch. In any case, there are few similarities between the Biblical flood account and the Greek accounts.
Woolley's clay deposits
Perhaps the most likely candidates for archaeological evidence for the Genesis flood are the various deposits of clay found in dig sites in what is now southern Iraq. These date from c. 3100 to 2400 BCE, which well satisfy the first requirement and also the second. However, given there were at least 4 separate flood deposits within 600 years, the description of a single, all-destructive flood does not fit. These seem like very powerful, very localized 100-year floods, rather than a single, wide-scale 1000-year+ flood.
The Flood Myth genre
In the end, I think the most probable interpretation is that during the time of the Sumerian flooding a literary genre centered on explaining the destruction of cities was developed. According to Genesis, Abram moved from Ur (a Sumerian city) to Hebron (a Canaanite city) and lived a few hundred years after the Sumerian flood events. Around that time, a number of flood accounts were recorded in Mesopotamia. The most complete version blamed the flood on gods who were tired of the noise that humans made. If the composer of Genesis wished to incorporate a flood narrative, he would have discovered difficulties reconciling that motivation with the motivation of a monotheistic, creator God. In the theology of Genesis, a number of details would need to be reworked in order to make the story work in the context of Abraham, Isaac, Jacob, and Joseph.
If we try to interpret the Genesis flood under the rules of modern historical records, we are reading into the account our own biases and assumptions. Ancient historians did not see events as containing meaning in themselves as we often do. Rather, they saw events as reflections or echoes of deeper truths. The Sumerian flood accounts explain those destructive events as the result of fickle and selfish deities. The Genesis account reworks that material to show the flood was a result of fickle and selfish humans. It would not upset early readers to learn that The Flood was actually an amalgamation of several extremely destructive flood events across a numbers of cities in the Mesopotamian flood plane.
God said He would destroy all flesh. That is why we find millions and millions of dead things buried in sedimentary rock all over the world. One factor that is often, very strangely, overlooked, is that fossils almost never form under normal conditions. They are the result of sudden catastrophes.
The problem with evidence for a flood is not the lack of evidence. It is the presuppositions we bring with us, that is, the lens through which we look at the world. If your presupposition is one based upon uniformitarianism rather than catastrophism, you aren't going to come to the right conclusions.
One side says sedimentary layers are deposited over millions of years, the other says they were put down, globally, by a flood. From what I have read, the evidence favours the latter. The layers are not disturbed as they would be if any was exposed for a length of time, and experiments with mixed grades of materials (i.e. sand, pebbles, stones, rocks) in large tanks of moving water have found that the water itself separates the different grades of material into different layers.
Michael's point about the Grand Canyon is a good one. For it to have been carved by a river, water would have had to flow uphill. The canyons were not initially caused by "uniformitarian" erosion, but actually carved by huge amounts of water running off sediments as the floodwaters receded. I live in the Blue Mountains near Sydney, Australia, which have similar sheer cliffs, very obviously not the result of a little water over a long time, but a lot of water over a short time.
If all this sounds difficult to believe, it's time to get educated on flood geology. My friend Tas Walker is a mining geologist who has a website dedicated to assessing the evidence without the bias of uniformitarianism, and with a biblical bias instead. Turns out the evidence makes a lot more sense (including the fossil evidence, such as large graveyards of dinosaurs buried in sediment in one hit).
There is more info here:
Believing in the Bible's chronology is a major paradigm shift, but it's neither impossible, not does it require shelving one's brain. I have another friend who designs satellites who is a young earth Creationist. These men are not fools. The fools are those who ridicule them without actually dealing with any of their very sound arguments. We can have total confidence in the Word of God.