Re: constructed sign language

FWIW, in ASL there is a historical change rule that causes asymmetric
signs to become more symmetric (roughly speaking*).

Far be it from me to claim anyone ought to be naturalistic unless they
feel like it (or that ASL is the reference grammar for all sign
languages), but I believe you will find that making one hand do one
thing and another hand a different thing to be very difficult to
achieve in practice, because it's a hard thing to parallellize in
thought. All sign languages I know of have these grammatical changes
either bundled together into the same sign (e.g. aspect is indicated
by a modification of movement) or do it syntactically (e.g. tense is
indicated by a modifier word before or after), rather than the hands
doing different things. The closest I can think of is a very unusual
case where one is signing two things at once under two different
persons, with right/left shifting, and only using half signs on each
side because it's desirable to emphasize the signs somehow or to make
the usual back-and-forth of role-shifting be parallel instead.... I've
only ever seen this happen in poetry / music interpretation.

Are you perhaps familiar with any natural sign languages? Are you
trying for naturalism in the first place (you may not be, in which
case this is moot)?

- Sai

* More precisely: signs change to become more central; to have both
hands have the same handshape or to have a dominant / base hand
distinction, with base hand having severely restricted handshape and
movement; to have identical or opposite movement; etc. See Klima &
Bellugi, _Signs of Language_ (1st book IIRC) for more info.