The moon causes our tides, but not in the way most people believe.
My answer below is belied by the this wonderfully detailed post, which explains exactly how tital forces playout, and debunks my ancient and cherished belief in how the tides actually worked.
There is no tidal bulge
Now from day to day, the moon doesn't move much (it takes just under 28 days for the moon to orbit the earth).
So how come the Moon - which is moving very slowly on a daily basis - can cause the seas to move a massive amount twice a day?
The answer is it doesn't.
I'm useless at drawing things, but imagine the earth as a large ball (soccer ball), and the moon as a ping pong ball.
Hold the "moon" out away from the "earth", now keep the moon in position but slowly rotate the earth around it's axis (simulating the rotation that gives us our day).
The moon isn't moving, the moons gravity pulls the sea towards it causing a "tidal bulge", there is a corresponding bulge on the other side opposite the moon, and no bulge to the left and right.
As the earth rotates, the moon stays where it is (for the purposes of illustration ignore the small amount it actually moves), so the bulge also stays where it is, one facing the moon and one facing away.
Now imagining this bulge, rotate the earth "one day", each part of the earth will move into the bulge facing the moon, then out of it, into a non-bulge area before moving into the bulge opposite the moon (approximately 12 hours later), then as the 24th hour approaches it's moving back into the tidal bulge facing the moon.
So, the tides "moving in and out" are an illusion, like "sun rise" and "sun set" the sun isn't moving, the earth is rotating and the sun appears to move.
Again with the tides, the "tide" doesn't move in or out, the earth rotates under the tidal bulge, giving the appearance of the sea moving, when it's the beach moving under the sea.
Lots of good explanations and nice illustrations here
Obviously I'm using approximations here, tidal frequency runs at something like 13 hours (I think) not 12, but this illustrates the general effect
So "moons" aren't going to pull your oceans in different directions, and not for that long a time.
Our tidal bulge does move, but it moves very slowly
I can't imagine how you could explain away shifting an entire ocean like this with tidal dynamics, sorry.