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At the risk of making myself very impopular on this site:

To me, inventing Chess variants is like 'inventing' integer numbers.
Make a string of some 100 digits, and the odds are overwhelming that you
are the first ever in this universe to have mentioned this number. OK, so
you can marvel at your own private number, but who cares? Pritchard was
quoted to say: Ït takes about 10 seconds to invent a Chess variant, and,
unfortunately, some people do'.

It is just like with the numbers, it had better be very special in some
respect that you point out, or it cannot be considered an invention at
all. The axioms of number theory already imply the existence of all
integers, and states that there is an infinity of them, so the fact that
you can name a few that no one ever mentioned before adds absolutely zero
to what was already known. AFAIK, there is no website where people can
post large numbers they invented. Prime numbers are already a bit more
interesting, but still so common that it makes little sense to post
everyone prime you discover. Unless it is the largest prime ever
discovered so far. (Did you know that about 0.45% of all 100-digit numbers
is prime?) Some numbers are very interesting, though, and entire books
could be written about their deep mathematical properties. This applies to
numbers like pi, Euler's constant gamma, the base of natural logarithms e.
(They are not integers, though, but the analogy would work just as well for
real numbers.) 

IMO, it is much the same with Chess variants. The 'axioms' of a royal
piece, translation-invariant piece moves and replacement capture imply an
infinite set of Chess variants, and the fact you can mention one (or a
hundred) explicitly is as meaningless as designing a hundred huge
integers. A Chess variant is only worth mentioning if it it has some very
special properties not found in most other variants, or solve some
problems found in existing popular variants.

With Chess pieces the situation is similar. A Chess variant can be
worthwile as a vehicle to exercise a novel piece, but only if the piece is
interesting. But also novel pieces can easily be uninteresting
run-of-the-mill constructs. Merely bringing up novel combinations of the
Betza atoms does not make a worthwile piece. Breaking the eightfold
symmetry gives even more pieces that could be useful on boards of limited
size, but so what? It woulkd only be of interest if it creates some
interesting irreversibility in play (such as with the Pawn), or a weird
color-boundedness not seen in other pieces. Or some intersting end-games,
where it is difficult, but nevertheless possible, to mate a bare King. New
capture modes or other side effects of piece moves could be interesting,
but have the disadvantage to make the piece less 'Chess-like'.

To demonstrate that a variat you designed has any such properties that
could make it worthwile does require a lot of analysis effort.