The second reference you gave is, I am pretty darned sure wrong.
It has been rather a lot of years since I read anything on this (half the people here were probably not born) but the reason for the two tides is NOT because the Sun is added in with the Moon.
IIRC the sun's gravity is a rather minor part of the tides.
The two tides are because there is one side of the earth where the Moon pull is somewhat stronger and the other where it is weaker.
The Earth and Moon revolve around their common center of gravity. This means that other parts are experienceing additional forces. Dammed if I can remember the details.
I would expect that Sylas will jump in with the complete details at any minute. I don't think this is worth the effort to google.
Without reading back over the thread isn't this about tides in a flooded world? My understanding is that they will not be bigger because the ocean is deeper. The bulge would be about the same size on top of the deeper ocean. In addtion, without land masses to stop the motion of the bulge around the rotating earth I think the tides would be more uniform and much, much lower than the high ones experienced in some parts of the world now.