Prone is a condition, and generally a condition is redundant. Damage is cumulative and generally untied to the condition. You can't knock an unconscious person more unconscious, but you can damage them more. You can't make a poisoned character more poisoned, but you can do more poison damage.
So in the spirit of similarity, I would say that yes, you can do the damage. You just can't make them "more prone". Ignore the saving throw if you wish, but the damage of the maneuver should stand.
You are giving the aggressive block feats too much importance in relation to the other two feats in this chain.
Keep in mind that both powerful shove and flinging shove are modifying aggressive block.
Let's go step by step: Aggressive block.
The triggering creature chooses whether to be moved or become flat-footed. If it chooses to be moved, you choose the direction. If the Shove would cause it to hit a solid object, enter a square of difficult terrain, or enter another creature’s space, it must become flat-footed instead of being moved.
This text is here to limit the enemy choice, not yours. You have no choice at all here.
Why there is a limitation like this? Well let's assume you make me (an enemy) hit a wall.
I take no damage (since you have only aggressive block)...
So why would I choose to become flat-footed instead of hitting a wall since the latter does literally nothing to me? (the same is for hitting another creature).
In short? With only aggressive block tossing an enemy against a wall is pointless.
Now going with the second feat 'Powerful Shove' it provides you two well distinct benefit.
- When you use aggressive block you can shove bigger creatures. Cool.
- When something is shoved by you against a solid object it takes damage
This feat do not overrule the fact that when you use aggressive block against an enemy it is the enemy who is chosing what happens..and that enemy is still limited to always choose to become flat-footed (mechanically the worst option for him in the majority of situations) instead of hitting a solid object or entering difficult terrain.
Now the last feat Flinging shove does overrule precisely the last sentences of the aggressive block feat.
When you use Aggressive Block, you can choose whether the target is
flat-footed or Shoved.
Now you are the one who choose what happens and since the limitation of aggressive block are not present here you have no more such limitations at all.
In short? Now you can throw off enemy from cliffs or towers (into water, lava..you name it) without a saving throw and the enemy must deal with it and yes, now finally you can shove him against the wall to deal him your STR modifier as damage.
Best Answer
You can Shove as long as it's away from you
As you noted Shove can normally only push creatures away, but there are various directions that would be "away" from the creature pushing (including North-West and North-East in your example). This can be further extended to directly East or West if you consider that diagonal squares truly measure 1.5 squares of distance like this for a 5-ft/square grid:
Considering distance this way gives more real-to-life results for a map, but the in-game rules for movement/spell areas (see this diagram of measurements) would have all of these values rounded down to the nearest multiple of 5 and allow for less possible directions of pushing if they happen to be directly North/South/East/West on the grid:
Regardless of measurement, a push to any square that is farther away from you follows the rules for Shove and would be legitimate.
I don't believe the line in Agressive Block "If it chooses to be moved, you choose the direction." means that you can ignore the result of Shove "You push a creature away from you". And even if it does allow you to ignore that stipulation, there still doesn't seem to be any rule preventing choosing a direction towards any adjacent wall/creature/etc to automatically give flat-footed if you desire.