How to reinforce this concrete wall that wasn't properly drained and is starting to lean 3/4" from top?
I don't believe a metal band across the back will do anything. A perpendicular brace would have to penetrate the wall to the front and have a broad bearing on the front and then go back into the soil inside. It would be a major undertaking and, unless it was artfully designed, an eyesore from outside.  I do think that a wedge of crushed rock behind the wall may help.

In your picture there appears to be a drainage channel in what appears to be a poured concrete footing right under where the crack is. This may be the cause of the crack because the block above is unsupported there. Unfortunately if the soil is tight clay, water will not drain well through channels under the wall. If there are more of these channels in the footing, you can expect cracking at each one. 

Visible drainage holes in the middle of walls are unsightly and so, if they are not necessary, are to be avoided, but it may be necessary in your case. Just putting in crushed rock in a wedge at the base of wall may not provide enough drainage. But I think they could be drilled later from the outside. The excavated clay soil could be used to top the crushed rock to direct surface water flow over the top of the wall.

(I see some people where I live putting in horizontal drainage pipes behind and at the base of engineered block walls connecting to unsightly holes through the wall when the whole wall is dry fitted engineered blocks pinned together. There is already drainage around each block.)

Edit after comment: For some reason I was thinking about a metal brace on the back of the wall not being effective. However, a metal brace across the top of the wall might be. This would be a flat steel bar held to the top with bolts going into holes drilled into the concrete filling in the cavity in the blocks. However, this would be costly and unsightly. The steel would rust over time and might be a hazard to a dog or a child.

When you have the base of the wall uncovered you might have to fill each of those drainage holes with dry concrete mix with small aggregate to support the blocks on top. And drill weep holes through the joints in the wall on the outside.

If you can, talk to the guy who built the wall and ask him if he would do some remediation. If this wall cracks and leans over, it won't be good for his reputation. You don't have to mention this explicitly, it's obvious. It could be the original customer insisted on an unreasonably low price and the builder did his best with the budget he had.