OK for April 9, JL is petty much toast in terms of capacity. NH (ANA) has availability, but that's not helpful to you in terms of QF.
QF25 DOES have some seats that night - 7? Well, hardto say - most economy class fare buckets are sold out with higher Flex ones only available and the seat map is quite full. Other options may be to go via MEL on the QF79 (to NRT) and there's also Jetstar out of both CNS and OOL that day that appear to have quite a bit of availability for sale at least.
The thing is QF's point of view on this in terms of "can they do this?" is more or less yes - as far as they're concerned, the supplier they purchased for you on your behalf (ie: JL) cancelled the flight/seats you'd booked. Due to it not being QF operated, their only real onus (again from their POV) is to refund you. They would far prefer that then opening up seats - specially on very full as is flights. Heck, if there's not 7 on a flight like the QF25, I don't think you'd want to be separated either - so that's another issue potentially.
However, I would at least ask the question - can you be rerouted onto QF or JQ services either QF25 that evening, or QF/JQ via one of MEL/OOL or CNS (with appropriate connections). Again 7 seats may be quite difficult.
In terms of moving you to the next "available" QF operated service - I mean what if that isn't till, I don't know, the Wednesday after? Is that even helpful when you have prebooked things (not to mention impact on time off work/school hols etc - making an assumption I know).
See with this being super peak time for flying and high demand airlines want to make money (hence no reward seats - even in economy) and it's super hard.
Would you be happy to take JQ (jetstar) if they offered it as an option? That MAY be something they could do more easily than on QF metal.
Looking at the JL52 flight on 9/4, you're not getting 7 seats on that flight released short of a miracle of such proportions I just can't even think of an appropriate analogy (sorry). I suspect availability around the whole of easter period and holidays will be similar and you won't get much joy there with the number of seats you're after (sorry).
I guess I would be prepared that a refund is all you are going to get at this point - one could argue and push via emailing execs and all the things usually recommended here, but in my view that all takes time, and time is in short supply for his. I would definitely, when next contacting QF, to be armed with acceptable options (eg: QF or JQ on April 9, and whatever else may work for you around those dates if possible). Being able to point agents to look at, for example, routing via OOL or CNS could help push them in the right direction. It's certainly a thought and best to be forearmed with potential options imo.
good luck.