I have been going mad and it is beyond me why it has to be so complicated.

A few info about our case:
Both me and my wife are EU Nationals (Cypriot) and have been working in the UK for at least the last 5 years prior to the babies birth, but we have actually been living and working in the UK for 13 and 9 years respectively. I thought I could apply for his passport but I got 2 months JSA between jobs which apparently disqualifies me and baby's passport application would be refused.
Whether that is true or not I don't know and if anyone here does it would be a great help. One Home Office document on Treaty Rights states that you can apply as long as you can prove you haven't been a burden to the benefits system. Speaking with their agents on the phone leaves me with more questions than answers.
Either way we decided to use my wife on the application as she has been working in a partnership as self-employed (her official HMRC status) for at least the past five years. Where we got stuck is in the supporting documents:
According to Home Office these have to be original documents.
No P60 are available as she is self-employed. Her employer doesn't issue payslips but instead what they call Annual Partner Statements. Can they be accepted?
Given originals are needed, any tax forms our accountant can send for us to print won't be accepted. So instead he advised we contact HMRC and get SA302, which are summaries of her self assesments for the past years. But given the baby has been born this month and the next tax return won't be filed until same time next year leaves us with a period from April 2016 - January 2017 without proof from HMRC at least. On top of that since the start of January 2017 she has been on Maternity pay as she had to give birth. Does that disqualify her also?
Bottom line is based on other members experience here what will Home Office accept as legitimate proof of Employment and Tax payments if P60 and payslips are not available? Will any official employer statements and proof of payment work? Are even original bank statements accepted? Is the fact that she's been claiming Maternity for the last month prior to baby's birth disqualifying her also?
Any light you can shed on this would be appreciated, I just feel that we and especially our baby is more than entitled for a UK passport based on the length of our stay and our status for over 5 years but cannot find a clear answer on how we can prove we are qualifying either for me or my wife.