There are serious problems making your ideas coherent here!  The notion of operad
was in large part intended to model kinds of algebras whose laws do not involve repeated
variables, do not involve diagonal maps.  Operads do not even model groups, in particular,
and that was intended.   Any $E_{\infty}$ operad models all spectra, not just connected
ones, the essential point being that the zeroth space of the spectrum associated to an
$E_{\infty}$-space $X$, no matter how constructed, must be a group completion of $X$.
There is no "the" $E_{\infty}$ operad, rather there are many interesting ones.
(There is an axiomatization of infinite loop space machines, due to Thomason and myself,
that makes this precise.)   If you want to model $E_{\infty}$ ring spectra using operads
only, you can make a mistake by trying to use just one operad, as I did over 40 years ago, 
or you can do it right by using two interrelated operads, one for the addition and one for
the multiplication, as I also did over 40 years ago. See http://www.math.uchicago.edu/~may/PAPERS/Final1.pdf
for a modern recapitulation of that early theory.