At the age of 8/9 my daughter was doing an hour each of ISTD tap, modern and G3 ballet as well as 3 hours of elite troupe for competitions. She's just taken her grade 4 ballet and modern, and grade 3 tap at just 11 years old and is studying grade 5 and 6 ballet at the same time as her other classes with the addition of lyrical but that's very unusual (the grade 6 ballet I mean). Hers is a very good ISTD school but even as one of their most talented dancers who's performing solos and on elite troupe they wound't have her competing in a contemporary class - she's too young. It's about emotional maturity and also contemporary isn't recognised as a discipline by All England until they are much older I *think*. That said you might find the bigger comps (rather than festivals) tend to veer towards more dance moms type entries and so you'd get very little one's performing "contemporary" but not to a great standard (American rather than recognised uk )
I would absolutely recommend her taking her ballet seriously and regularly in line with her school (without skipping grades and in good time to refine things as they need to be ) and building up lots of classes and it will give her more strength, discipline (muscle wise) and technique which will help her stand out even more. All that said she's done SO well with her musical theatre what is their take on it - do they think she needs more dance ? I think if you were to submit a video for Matilda ensemble and she was good enough they'd not worry too much about the grade 4 level particularly if her cv said she's reached finals before. Did you go through an agent for her last audition? Perhaps ask them whether they feel grade 4 ballet is essential. What do her dance school think about her working towards grade 4.
As for solos, you do pay for the extra lessons and also for the entry fees for festivals etc . They get a HUGE amount from solo lessons in any discipline so I wonder whether you might instead ask for her to have a ballet solo instead or aswell so she can compete with that and see where she sits in that discipline across other schools best performers? Might help you decide. Sadly as you rightly say it's expensive and kinda unfair on kids who can't afford it but most parents will find a way .....
I hope I've helped, and udnerstood. She sounds super talented be great if your school could accommodate her for what she wants to do. x