Though I'm not involved with B737 maintenance, I am involved in a "cracked forging" inspection program with another type. In my opinion, in terms of a primary structure forging the only "repair" which might be approved could be dressing out of a very tiny crack, otherwise it will be repair of the airplane by replacement of the cracked part. I'll be surprised of a crack so small to be permitted to be dressed out could be detected before getting too long to require part replacement. It is generally otherwise not possible to "repair" a primary structure forged part (as by adding an element to share the load across the crack). A reference to "repair" [of the airplane] will likely be by part replacement. Letting alone the magnitude of the task to replace the pickle fork, another concern will be the availability of replacement parts. Industry can hope that Boeing had a large run of forgings made, and they sit either partly or fully completed. As forgings are a long lead time & and special process part, that are commonly made in batches, rather than as needed.
A forged part may be incorporated in a primary structure design, because that single part is a very efficient means to carry the load. If that part cannot carry the load (because it has become cracked), there typically is not a parallel load path available within that space or attachment to carry the load via an alternate path, so putting a strap across the cracked area is not a likely repair. By the time you did that, you'd have to bypass the entire design load into the same fastener holes, so you may as well replace the defective part.
The reference to an FAA or Boeing approved repair is a subtle reference to the fact that there is no other approved repair scheme to be found - you must request an approval for the proposed repair from either the FAA or Boeing. Otherwise there would be a "repair in accordance with...." statement in the AD. Perhaps in the future there may be, as suggested, but not yet. And, cunningly, the AD wording requires a defect found to be reported, because it serves industry well to have the data about defects. This because I expect that the Boeing maintenance manual might already describe or allow repair of the airplane by replacement of a defective part. So if an operator found a crack, and had a replacement part in stock, they might be able to simply replace the defective part in accordance with existing Boeing instructions. That's fine, but the initial defect must still be reported for statistical reasons.