First of all, thanks for all your input! There were many things I would
never have thought of. Now some conclusions (mainly thinking aloud):

It would probably be good to treat 'gating', where introduction of a
piece takes places in combination with moving another piece, distinct from
true drops, which leave the remainder of the board unchanged. For gating
there is the choice to consider it as a side effect of the move of the
piece that was already on the board, and this seems the most convenient way
to do it. (In my Betza 2.0 proposal I had already introduced a move
modality 'u', which could unload something on the square indicated by the
Betza 'atom' to which it was prefixed.)

The true drops could be considered a special kind of Betza atom, and '@'
would be a good notation for it, as in standard algebraic notation drop
moves are written with it (e.g. P@c6). Dropping on empty squares only could
be written as m@, with the usual Betza modifier m. The power of Betza
notation is in clever choice of defaults, however. Where board moves almost
always have modality mc, which is thus default so it never has to be
written, it is very unusual to allow capture through drops. So for the @
atom, m could be defined as the default modality.

Then there is the concept of the 'drop zone'. In cases where this zone
consists of a few squares scattered over the board, there seems no
alternative to actually listing them. In Betza 2.0 I introduced the idea of
a 'limiter', which could be put on a modality modifier, like c{N,B}A for
a move that could only capture Knights and Bishops with an Alfil move. This
is a bit of an awkward notation, however, so for the more common cases,
where the drop zone is the entire board with the exception of some ranks at
the edges, I would like to have something simpler.

One method would be to write the range of ranks where the piece can be
dropped, e.g. 1-7 for Shogi Knights. This conflicts with the use of the
dash as chaining operator in Betza 2.0, however. It would be nice if we had
to write only a single rank number, for then we could write it behind the
atom: @7. This has similar syntax to W4 for a range-4 Rook. In fact it
would allow a similar interpretation, when we see the drop move as a move
that starts just in front of the board (on rank 0, as it were), on an
arbitrary file, and slides forward from there onto the board. The number
behind @ would then indicate the maximum rank it could reach. Like in the
Bex proposal for extension of Betza notation, a leading 0 on the number
could indicate it does not specify a maximum, but an exact number: @08
would mean 'drop on 8th rank only'.

Problem with this is that it is difficult to exempt a low rank from
dropping, as is needed for Crazyhouse Pawns, which can only be dropped on
ranks 2-7. This would then need an exhaustive listing @02@03@04@05@06@07,
which is pretty ugly. The problem is similar to that of 'skip-sliders'
like the Heavenly Tetrarchs of Tenjiku Shogi, which move as a slider after
skipping the first square (e.g. t(D,R) = D, then R in original Betza
notation). Another problem is that the dropped piece should be able to
reach any empty square within the range, even if there is blocking. IIRC
original Betza notation described a piece that could jump an arbitrary
number of obstacles with a 'jj' prefix. So mjj@7 would do it for Shogi
Knight drops.

Like the 'm', the 'jj' could be made default in absence of an explicit
single 'j' or 'n'. This offers the interesting possibility to specify
'non-jumping drops' n@8, which could drop anywhere upto the first
obstacle, but not beyond it. Such a drop mode was not mentioned here, but I
could imagine it would be a useful restriction on drops, to not make them
too aggressive. A drop on ranks 2-7 could be written with the Betza
'then' notation as t(@02,jjR5), i.e. initial drop on rank 2, followed by
an arbitrary jumping forward Rook move of upto 5 squares. Still not very
elegant.

There seems to be no obvious way to specify further restrictions, such as
on the number of Pawns per file, the number of color-bound pieces on the
same color, etc., in the Betza spirit. Perhaps some extra modifiers could
be introduced for such restrictions, but the available letters are already
almost exhausted. Because directional modifiers make no sense on a drop,
they could be reused for other purposes there. (It is already the case that
the meaning of directional modifiers depends on the atom that follows;
'fr' in frW means something different than in frF or frN.) So 'f' could
be taken to mean the drop is not allowed if there is already a piece of
that kind on the file, and 'b' that it is not allowed if it is already on
the board. 'ff' could be taken to mean there can be upto 2 on the file,
etc. 's' could similarly stand for 'same color square'.

This would make Shogi Pawn drops f@8, Shogi Knight drops @7, Tori-Shogi
Swallow drops ff@6. Hey, that is not so bad!