Hi
I also play the accordion. I am the current South Pacific Champion for the 12 yr age group!! I've been playing since I was 7yrs old
Here in New Zealand you can take exams run by 2 examining bodies - the New Zealand Accordion Association or the Australian Accordion Association.
There is a proper syllabus etc. The aurals are identical to the ABRSM and the same system applies in that you can't progress past gde 5 without the equivalent gde 5 theory exam.
I am about to sit my gde 6 - to give you an idea I am playing Dance of the Comedians by Smetana, Mattinata by Leoncavallo and Valse Triste by Sibelius. There is also a Czeny study and a heap of scales ( including free bass ones) Additionally there is a section where you have to discuss the history and operation of the accordion so all in all it is quite a through exam and easily equates to the standard of any other instrumental exam at the same level ( and I've done a few!!)
I'm sure a similar exam system must exist in Europe ... otherwise come and visit - NZ is a great place You could stay with us