Yes, dealing with the Home Office can be very confusing. Generally applying for a visa prevents you from becoming an "illegal resident", but the COA is not a visa.

Instead, I think you should make an application under European law (EEA2). You will then receive a certificate of application a few weeks later, and with that you should be able to leave the UK without him being suspected of overstaying his visa. You should send the application as "signed for", so that you have proof of the Home Office receiving it, and it is sufficient to include copies of your passport. It would be nice if it is received before the visa expires, but technically that is not necessary. The postal strike does not help, and I would plan in some extra time for that.

Processing the application usually takes 6 months, so it may not happen before you get married. This could be an advantage, because as an unmarried couple it is quite possible that your application is refused, unless you can show that you have lived together for quite a while.

I assume he can get a tourist visa once he gets to Spain. Getting back may be more difficult: the UK system does not work very well while an EEA2 application is under way, even in a clearcut case. Luckily being from New Zealand he doesn't need a visa to enter the UK, so it might just work.