Not an RAD expert (about a term of RAD sometime in Grade 4, I think.) I did ISTD Imperial and my children do Cecchetti and neither of these boards include character in their classical ballet syllabus. If you're looking to move schools and your daughter doesn't enjoy character it might be worth considering choosing one that teaches an ISTD course. In the middle to higher grades there doesn't seem to be a great deal of difference (character dancing aside) so she wouldn't need 'catch up' time. Last term my DD's dance school took over a small dance school that taught RAD and the 4 girls that came into her Grade 4 class have fitted straight in.
For the June exam - have you checked out the RAD website? There's good information there and details about workshops and masterclasses that your DD might be interested in (depending on whereabouts you live and how rich and generous you're feeling.
Bear in mind - nearly distinction is still very good but I do understand her frustration. DD and DS both got near misses (A is the top grade in Cecchetti) last summer in Ballet (which they love) and this year got high 'A's in Jazz which neither of them work half so hard at.