Writing letters
I assume that you have addressed your grievance to yr Subordinate Commanders (officers) - they should be able to make arrangements to reimburse you if JPA is really causing you hardship (and £2.4k sounds like hardship to me). If you haven't done this, do so first, (ignore this warning at yr peril) using a Gen App to request an interview, if you still have such a thing, then it's on record.
To get the attention of people outside the service, all that is required is a simple 3 paragraph letter.
Paragraph 1: state the background to the grievance/issue you want him to investigate. State who you are, an SAC at RAF xxx, and you are using a new admin system, introduced on Apr 1, and you think he might find it interesting to investigate how things are going.
Paragraph 2: Provide detail he can use for his enquiry. Relate your experience (briefly; lack of suitable functionality in the software, unobtainable enquiries desk, lack of access to terminals, lack of any offer to reimburse you, reaction from chain of command, refer to this blog with a http:// , he will be able to access this site from HofC)
Paragraph 3: This is the para for asking what you want him to do. In your case it's probably to press for immediate substantial improvements in the arrangement for paying allowances pending improved JPA functionality.
I say again, use your officers first, before you go this route. Best of luck.