My concern with Bromley high is mainly that they don't prep you for the grammer or more selective schools at 11+. A real dilemma for me too whether to move from Bromley all the way to Dulwich
If your long game is a good girls grammar at 11+ or even to have the option, I'd choose Bromley, not bother moving either. You wont feel crippled with guilt leaving Bromley for a grammar, a good few girls will at 11+, but once in Jags, it will be hard to leave given its prestige and name, less girls would move for a grammar school.
If you're happy and able to pay till 18 , go with Jags.
In an ideal world you'd be at a prep that prepares for grammar school.
There is no wrong choice with schools like these, but reading between the lines, I think your gut is telling you grammar is the sensible choice at 11+. If so, Jags or even Bromley isn't suitable.
If you do move for Jags and want to live within walking to the school, or very short car ride, then you get a lot less brick for your buck in Dulwich compared to Bromley, even in the million+ bracket Dulwich gets you pretty ordinary looking 3 bed terrace. 4 to 18 is a huge financial commitment, for both schools.
On the bright side, your DD has done amazingly well, I suspect she'll thrive at either or a good prep.
Would anyone pick Bromley high over JAGS in any scenario?
If I thought Bromley was the better school for my daughter and she'd be happier there, yes. Bottom line its gut feel, and as long as you've got both eyes open, you can't really make the wrong choice.