Some things to take into account:
- As the SEP article on supererogation notes:
Another issue raised by attempts to subject the concept of supererogation to some version of the general schema is that of “offence” or “suberogation”: if there are non-obligatory well-doings (supererogation), are there also – as their mirror image – non-prohibited wrong-doings (“permissive ill-doings”)? ... Some philosophers (Chisholm 1963, Richards 1971, Forrester 1975, and Driver 1992) were attracted to the logically neat symmetry of supererogation and suberogation, but a critical examination of this artificially invented category demonstrates both the difficulty in filling it with content and flaws in the general schema itself (Heyd 1982, Mellema 1991).
So with respect to the deontic operators, it seems that there is a moment of asymmetry (though see here for considerations regarding "permissive suboptimality"), in line with your ideal.
Moreover:
- There is a family of set theories, known as "positive" set theories (see also here), which feature no negative formulae (in some useful sense of the phrase "no negative formulae"). Suppose that set theory is "the foundation of mathematics" in some tractable way. So, a mathematics founded on positive set theory might support conceiving of a possible deontic order with weaker negation conditions.
It would be impossible, however, to do away with all negative representations in this connection. It is a priori, and mostly innocuous, that FRA = OB~A, so to get rid of FR would require getting rid of mere ~, which seems silly, and as applied is anyway "disproven" every time someone thinks through FR sincerely. Or how should we be expected to magically forget the entire history of moral language as we know it? There are those who dislike the use of the word "evil", though, for example, so that again, we might not have a fully uni-directional moral spectrum in play, here, but we do seem to have one weighted more towards the good (which is as it should be, after all).