You've noted what I've noted before in this forum, if you say that
"(V)SWR" is the SWR that would result if the forward and reverse waves
at a particular point on the line (the point at which you've measured
rho) were allowed to develop a voltage maximum and a voltage minimum
(or a current maximum and minimum). I happen to believe that is more
in keeping with the original meaning of (V)SWR than the formula which
says VSWR=(1+rho)/(1-rho).

Of course, this all gets quickly into people trying to assign physical
significance to rho which is not really there; they get confused when
rho1.

If you are clear and consistent with your definitions, I don't see that
any problems result either way. I happen to believe that the formula
you came up with is a better one than the one you commonly see in
texts, but I also agree with Roy that you'd better be clear about it if
you use it, because it goes against the commonly accepted grain. On
the other hand, I've seen texts that derive it in the same way you
have, which come up with the "wrong" answer (without the abs) based on
their initial premises.

Cheers,
Tom