Non-muslim Malaysian marrying a foreigner. Options?

I have a peculiar situation. I (26M) am a Chinese Catholic, and I wish to marry my girlfriend (26F) who was born in Iraq as a Muslim, but secretly a practicing Catholic.

As we know, marriage is not straightforward for us as JPN explicitly requests the Iraqi for a letter from their embassy that states their religion, and Iraq is like Malaysia where Muslims can't convert out. I'm wondering if there are any options for us that we haven't explored.

1. Could we somehow... get it done? (Maybe someone out there has a solution or a lead).
2. Could we register in another country and re-register again here? (I've checked and the answer is no unless I'm wrong).
3. Migrate: Honestly, this is our only real lead, but the issue is the migration climate seems to be increasingly constrictive by the years.
4. Final resort, save money to buy a passport ($100,000 USD). Then we'd be almost 40 and penniless, but hey...

Posting this on a throwaway, this is quite a Hail Mary and I'm wondering if someone out there knows some way. I'm still hopeful that God provides.