Yeah but no but...

I did wonder as I read the article what the numbers are for people living on sediment or coral.

As you say, the sediment is produced by the increased rate of erosion by the sea on the new shoreline. This is the process that ultimately reduces mountains to atolls and then submerged reefs. The increased sea-level actually produces an increase in entropy which is why erosion speeds up.

The idea that ones home might be reduced to a mud-flat before being completely drowned seems a little better than that it'll go under in one smooth event, but only a very little.

Solar cycles and weather are certainly connected (in some way not yet understood), but not in the fine detail that Mörner claims. 1815/16 was Tambora, not sunspots. It is not unusual for the assumed effect of the sunspot cycle to be contradicted by temperature measurements on the ground, as indeed it is at the moment.