This works, but some of the details differ
You have a lot of steps in your description. To see if each one of them is conforming to the rules of Echo Knight (all p. 183, Explorer's Guide to Wildemount), let's break it down:
Once it’s my turn I teleport with my echo, swapping places. This uses 15 feet of movement, but this does not provoke an attack of opportunity since it’s a teleport.
As a bonus action, you can teleport, magically swapping places with your echo at a cost of 15 feet of your movement....
I then move my echo around the enemy (5 feet down, 10 feet to the right) without breaking contact so that it is now located 5 feet down and 5 feet to the right of the enemy. I move myself 5 feet to the right so now I am 10 feet to the left of the enemy.
On your turn, you can mentally command the echo to move up to 30 feet in any direction (no action required).
I then make one attack with my glaive (d10) at reach, one attack with the blunt edge at reach (the d4)
You are taking the Attack action. This is from Polearm Master:
When you take the Attack action and attack with only a glaive, halberd, quarterstaff, or spear, you can use a bonus action to make a melee attack with the opposite end of the weapon. ... The weapon's damage die for this attack is a d4, and it deals bludgeoning damage.
Because you already used your bonus action for the turn to teleport, and making the blunt end attack also would require a bonus action, you can attack, but not also attack with the blunt end — you only have one bonus action per turn (credit to MDJ for catching this).
...then decide to use the Unleash Incarnation to make one additional attack with my echo (d10 from the echo’s location)
Whenever you take the Attack action, you can make one additional melee attack from the echo's position. You can use this feature a number of times equal to your Constitution modifier....
The melee enemy moves 5 feet to the left to attack me, but I use my reaction for an attack of opportunity (d10) from the echo to the enemy.
When a creature that you can see within 5 feet of your echo moves at least 5 feet away from it, you can use your reaction to make an opportunity attack against that creature as if you were in the echo's space.
I don't think this works. If you have a polearm equipped, you cannot attack an enemy that is moving within 10 feet, because you have 10 feet reach and that enemy is not leaving your reach. So if you can make an opportunity attack as if you were in the echo's space, in that case you cannot make an opportunity attack via the echo. Otherwise that phrase "as if you were in the echo's space" was not needed -- the rule could just tell you that if a creature moves 5 feet away from the echo, you can make an opportunity attack from the echo's position, the wording used for making attacks as part of the attack action (quote above).
I think this is the most interesting part of your question, because the way the feature is worded means that you never can make an opportunity attack via the echo with a polearm -- you only get to make them if a creature you can see moves from within 5 feet of the echo to more than 5 feet away, and that does not trigger one from a polearm. You don't get to make them if the creature moves out of the reach you had if you were in the echo's position. I think a DM ruling to read it like that instead would likely not be unbalancing.
There is also a tweet from Jeremy Crawford on the matter, in response to a question if you can attack with reach through your echo if you have a reach weapon, confirming that does not work:
The Echo Knight's opportunity attack feature has a range of 5 feet. Your weapon's reach doesn't apply. The rule would refer to that reach if it was applicable.
Good rule of thumb: "within X feet" means within X feet in D&D rules.
Jeremy's tweets are not official rules content anymore, however. It's not entirely clear to me if by "Your weapon's reach doesn't apply" in the context of the question is meant to say you just should ignore the reach property altogether, and you could attack if someone moves from 5 to 10 feet, but you maybe could read it that way. That is not what the rules text says, but I think ruling to play it this way would also not break anything badly, just as ruling to allow reach would not.
However, here this does not matter -- you can just make the opportunity attack from your own space, because the creature is moving into your own reach, and you have polearm master's other benefit:
While you are wielding a glaive, halberd, pike, quarterstaff, or spear, other creatures provoke an opportunity attack from you when they enter the reach you have with that weapon.
On my turn I move 30 feet up with my movement. This causes my echo to disappear since I am more than 30 feet away.
No, it doesn't:
If your echo is ever more than 30 feet from you at the end of your turn, it is destroyed.
After you moved, it is not yet the end of your turn, so the echo is not yet being destroyed. However, it is not necessary that it is destroyed because:
You can use a bonus action to magically manifest an echo of yourself in an unoccupied space you can see within 15 feet of you. This echo is a magical, translucent, gray image of you that lasts until it is destroyed, until you dismiss it as a bonus action, until you manifest another echo, or until you're incapacitated.
so when you continue:
I then manifest an echo 15 feet up from me. I use its movement to bring it right in front of the ranged enemy. I use my action to attack (d10), then spend another use of Unleash Incarnation to attack again (d10).
The manifesting will take care of destroying the old echo. Because the echo is only destroyed at the end of the turn, you also can move it further than 30 feet away from you (here, 45 feet including the 15 feet from manifesting and 30 from moving it) and attack with it, without it being destroyed.