If you rotate, it is clockwise.
It is basically a circle.

You can choose to move in a diagram like this

Table
_____________
. . . . .< ---------->forehand
. . . ^
. . . |
. . . | must prepare backhand
. . . v

This is only going to work for the first few balls. Afterwards, you adapt. This favors one close table player and one mid-distance player. This movement seems okay if the one close to the table cannot move much.

If you don't want to block each other at all, don't rotate. Do this instead:

Table
_________
. . ^ ^
. . / . . \
. ./ . . . \

This is exactly the same as the lefty-righty movement. One of you will have to abandon your corner and start using more backhands. basically, the lefty on the left becomes a righty.

You take turns covering the table. The one more comfortable with backhand should take the position on the right. Ideally, the lefty on the left should know the crossover step footwork well so that they can cover the far right corner. Also, the lefty on the right should make shots going to right corner (the place where you serve to in doubles), so that the lefty on the left won't be too far out of position. The lefty on the left should try to hit towards the left corner so that the lefty on the right wont be out of position

All in all, one of you will have to have a decent backhand, and one of you will have to know how to crossover step. the crossover step player should be using a lot of forehand shots (that would be me!  crossover step is fun). Ideally, you both aim for the best corner. If the lefty on the left tries to hit a forehand cross court, the lefty on the right should get ready to run and crossover. when the lefty on the left serves, the lefty on the right should make sure to cover the far corner. lots of people will aim there.

The last one is seems preferable, since one of you wont have to change your doubles movement. only the lefty on the left will have to do things differently.