Hello
What you describe here is really messy.
If you read the guidance about Lounes case here:
https://assets.publishing.service.gov.u ... idance.pdf
(form page 15):
You are not a "
Relevant British Citizen" for the purpose of Lounes immigration sponsorship. When you obtained the British citizenship in 2007, your country wasn't part of the EU at that time and you weren't exercising Treaty Right and you never did. When Croatia joined the EU in 2013, you were already British for 6 years.
this small issue because that's not your fault
This is not a small issue but a big one as it concerns eligibility criteria.
Also, I don't know where this concept of "not your fault" came from. Because it can open the door to wild things. Why not considering a Nigerian national as EEA national because it's not his fault he wasn't born in the EU and becoming an EU national? You see, we can take it far.
There is also the risk that your wife breaches legal stay in the UK which makes her ineligible for British citizenship for 10 years.
Get a credit card, pay £2400 and apply for ILR if you still can.