The Greenwich comps have improved a lot!
We looked at both options for our dd, so saw a LOT of schools in SE Greenwich/Bexley last year.
As well as Crown Woods College, which was on Tough Young Teachers recently
we were impressed by Eltham Hill's beautiful new buildings and rising standards, and by the Heads and our student tour guides, at both schools. We also looked at St Catherine's RC Girls in Bexleyheath, which has some "other faith" and community places. Another fantastic mixed ability school with a great atmosphere.
I do not get the impression that any of the Bexley grammars are as pressured as the nearby N Kent ones, nor as the superselectives in Bromley. I think they are all the better for it, frankly. I think there is a broader ability range at the Bexley grammars and they are all large schools which also helps.
The grammars, as you might expect, offer a wider choice of more academic subjects, the comps offer a core academic curriculum and more choice in the applied vocational subjects at GCSE and BTEC.
We have an older child at DGS, and that suits him perfectly. Our dd would have found DGGS or Newstead Woods completely daunting. Like your dd, she sometimes lacks confidence.
Bexley GS was our preferred selective option for dd and she passed the Bexley test so that is where she is going. We feel it is a happy, high achieving school with little evidence of damaging competitiveness or pressure. We know other families who love it for their children. IMHO you probably won't hear much different about the other three Bexley grammars, including Townley, they all seem to be basically very good schools.
I would have a good look at all the local schools, with an open mind, and with your dd. See what she thinks! There are definitely plenty of good choices for girls currently round here, selective and mixed ability.