Earlier this year there was an errata for charge that removed the destination from "the nearest square from which you can attack the enemy" to simply being where the target is. If playing as written on the errata, you can actually choose whether you want to charge to reach or charge adjacent, and in fact you can actually charge something that is just out of your move speed, but will still be within reach at the end of your charge.
The actual wording now is:
CHARGE A TARGET: STANDARD ACTION
Target: When a creature takes this action, it
chooses a target. Determine the distance between
the creature and the target, even counting through
squares of blocking terrain (Dungeon Master’s Guide,
page 60), and then follow these steps.
Move: The creature moves up to its speed toward
the target. Each square of movement must bring
the creature closer to the target, and the creature
must end the move at least 2 squares away from its
starting position.
Attack: The creature either makes a melee basic
attack against the target or uses bull rush against it.
The creature gains a +1 bonus to the attack roll.
No Further Actions: The creature can’t take any
further actions during this turn, except free actions.
Thus with this errata, you can always charge to adjacent square regardless of reach. Personally I would rule that the first half of Avalanche Reaver, the "push target of the charge one square" will work as long as you hit with a charge attack. The second half, which is the shifting bit, will only work when you were charging to adjacent.