They haven't given you much time to respond so a return visit is probably not possible.
Playing devils advocate....
From the sound of things, your first choice of CHG was based on her sister being there, closeness to home and convenience of bus routes. These are concrete reasons. It's incidental that her best friends are going there.
For Handsworth, she basically felt a part of it based on the Induction Day. As reassuring as the Induction Day is, I don't think it's that important especially as your older daughter can fill her in on the basics of CHG, I.e where to go and what her teacher looks like etc. there are plenty of "icebreaking" activities in the first few days so she will get to know her class even if she didn't meet them on induction. From what I remember about CHG the school doesn't organise anything between Induction Day and September and I doubt the girls will remember who they spoke to that day.
Regarding journey times, would she be fine with a longer journey in winter (cold, dark alone) rather than a shorter one with her sister for support for the first few years? Seven years is a long time to consider.
The Ofsted for CHG is very outdated and I wouldn't use it to judge it. I have met some lovely teachers there who have really inspired my daughter (there was only one I didn't like which is quite good for me!). Handsworth is more of an unknown quantity despite the Ofsted unless you know a girl there who can give an "insider view".
DD doesn't consider CHG to be any more competitive than her primary. All secondary schools have some competitive children and it's up to your DD if she becomes a part of it or detaches herself as mine do.
I think you might stick with Handsworth as you have said your DD "knows exactly what she likes and is strong minded" so she might not be open to the idea of CHG. I overruled my own DD on the CHG v KEHG debate and she actually thanked me for it!
Incidentally, there isn't a correlation between score at 11+ and how the girls do once they are in the school, so don't worry about it