I wish that you would quite making this argument. It is simply not true. Though there were rapid sea level rises on a geologic scale. they were not so rapid on a human one. Even at the fastest it was not rapid enough to cause the flooding that you described:
"Two deglacial MWPs were identified at Barbados [
Fairbanks,
1989]. Whereas MWP-1A was identified at Sunda Shelf [
Hanebuth et al.,
2000] and Tahiti [
Deschamps et al.,
2012], MWP-1B was not captured in Tahiti bore hole cores [e.g.,
Bard et al.,
2010], leading to controversy over its authenticity as a feature of the post-Younger Dryas global sea level record [
Lambeck et al.,
2014]. MWP-1B was first identified and defined as a 15 m jump in the Barbados sea level curve centered at 9500 14C yr B.P. (11.3 kyr B.P.), based on dated corals from two cores [
Fairbanks, 1989,
1990]. U-Th-dated
A.
palmata data in six cores now confirm and better constrain the amplitude and timing of MWP-1B as a 14 ± 2 m jump (Figure
S2), occurring between 11.45 and 11.1 kyr B.P. with maximum rates of sea level rise approaching 40 mm yr−1 (Figure
1a)."
<bolding is mine><rats, no it is not, I guess I cannot put copied text in bold, read the very last sentence>
Please note, the fastest level of sea level rise, and it lasted for about 350 years, was around 4 centimeters a year. Call it two inches a year if you are use imperial (actually only 1.57). That is fast if you have a city that is right one the ocean. In 25 years the buildings closest to the sea would probably be flooded. That is a meter of rise. That is not a catastrophic flood.