Hi... welcome to you and Soren!
Do you think the self stimulation of jumping etc (stimming) is related to starting school? We were aware of sensory issues with my son before he started school but I only ever saw him stimming once he'd started school and got over-excited and hyped in a way that didn't seem to happen in his preschool (a lovely gentle place). His teacher in his second year of school (dreadful woman, very unprofessional on many levels... don't get me started!) announced he had to "be autistic" on the basis of his stimming. Children get really hyped by other children and the school environment with its busy-ness and noise can just overload children - and no it's not predictable or consistent, some days the "coping cup" takes longer to empty. There are some people who think that the sensory stuff is at the basis of a great deal of what is "autistic" behaviour.
Sometimes it can be helpful to approach it from a behavioural analysis direction - try and see what might be a precursor or trigger. Start a daily journal: How did he sleep? How did breakfasting go? The preparation for school and trip there? You'll need to get the teacher on board and hope they are intelligent observers (our teacher wasn't....) - can he/she see a link between the days he copes with the singing and the days he doesn't and what came before?
OT can be really helpful providing really strong physical stimulation that impacts deeply on the big joints (hips, knees, shoulders) in particular that is wonderfully organising and calming. Carol Stock Kranowitz's book "The out-of-sync child" explained it all so well - really worth reading about sensory issues. Trampolines are great! Music with a big beat can sometimes work well when they're bouncing, a good solid, regular rhythm.
Anyway - some ideas from me! Let us know how your OT appointment goes and keep asking questions.

BusyMum
Sydeny, Australia