word order - Using 'for' as a coordinating conjunction at sentence beginning

As I understand it, 'for' is a coordinating conjunction. Learning German as a second language has taught me specifics about reforming sentences, but it is an awful lot less common in English. If I were to rearrange the sentence: "I ate lunch, for I was hungry," so that 'for' was the first word of the sentence, by my reckoning I should end up with "For that I was hungry, I ate lunch." Does this new sentence have any grammatical errors? I inserted the word 'that' after 'for', because without it the sentence didn't sound right. Should I have? Is there a rule for that? Thank you in advance, an aspiring author.

Additional Information:
I am not having problems with the sentence, this is a general question to increase my knowledge of the manipulations of coordinating conjuntions.

Answer

You are right that for is a coordinating conjunction, the first of the so-called FANBOYS. But you cannot move a coordinated clause (starting with a FANBOY) to the front of a sentence:

I was hungry, so I ate.

*So I ate, I was hungry.

It is the same in German:

Ich habe gegessen, denn ich hatte Hunger.

*Denn ich Hunger hatte, habe ich gegessen.

However, you can move a clause with a subordinating conjunction to the front:

Because I was hungry, I ate.

Da ich Hunger hatte, habe ich gegessen.