If the Interactive Diagrams had a rule that pieces could move out of the "hand" with an iU move (or perhaps an atom specifically designated for the purpose), that might be a more generalized solution.

This is one of the things that has been on the to-do list for very long: an atom to indicate dropping. The plan was to use @ for this as if it were a capital. Of course directional and some other modifiers and ranges would be meaningless in this case, so the corresponding lower-case letters could be recycled for drop-specific meanings. Like j meaning that you cannot drop on first rank (somewhat similar to its use for ski-pieces, if you imagine the dropped piece to come from behind the baseline), and a range behind the @ indicating the maximum rank you can drop. The f (for 'file') could mean that only a single piece of the type can be in a file (and ff two pieces), while the s could limit you to a single piece per square shade, and b for the entire board.

The problem is that it doesn't bring very much as long as the AI doesn't know how to use the drops, and currently it doesn't search deep enough to see the advantage of drops, and will be overwhelmed by the large number of drops that would in general be possible. Limitations on what you can drop in the same file or shade are by definition a legality matter, and since the Diagram highlights all pseudo-legal moves you would not see that even in manual play. Limitations on the ranks you can drop can now be specified by a morph parameter (exempting the normal moves), so for that you won't need it either.

And then there is the issue of evaluation. The AI uses the Pocket Knight in a pretty stupid way, dropping it as quickly as possible. While the best use is of course to keep in in your pocket as long as possible. This behavior comes from the built-in drive to centralize pieces, and in the representation here the Pocket Knight is furthest from the center. So it gets an enormous bonus for brining it into play.

This exposes a flaw that might have a general fix: in a sense pieces that have an initial move are not the same pieces as those that no longer have it. Basically the first move always is a demotion. Now the value of a one-time move is of course not nearly as large as when you can use it forever. But it would contribute some, and especially when it is an extremely powerful move like U, even the small fraction it contributes can be significant compared to positional bonuses like centralization. So moving pieces with initial moves should incur a penalty, the magnitude of which could be calculated by repeating the value guestimate with the initial move enabled.