I also take it to mean that it's either work others are often unwilling to do, or something that's really difficult, or something that I've been wanting for a long time but haven't gotten anyone to help me with.

For example: There's a fluorescent light above my desk that flickers and has been driving me crazy for years. I can't get facilities to fix it because they need a ticket that's approved by management and has an approved budget, and all their other tasks are more urgent.... so it slowly drives me mad for a year. Finally, a facilities person says "You know what... I'm not supposed to do this without management approval... but I'll just fix this real quick and it'll be our secret" ..... Me: "Oh, thank you, you're doing God's work"

Ah, yeah if it had been worded like that I'd have recognised it as the idiom, but hadn't occurred to me it could be an unusual wording of that idiom.

I suspect the saying may be more common in North America. I’ve never heard anyone say it in Ireland – though American phrases and spelling are starting to become more popular thanks to the Internet and the success of American tech companies.

Also, relentless dominance ("cultural colonialism") of film and TV for decades.

Yorkshire is known as God's own county; I don't think that is an American import.

nah. far easier to be offended. that'll show 'em.

Maybe I'm also misunderstanding you, but if that comment was aimed about me then I wasn't remotely offended by somebody mentioning god, I just didn't understand if they were literally talking about the God they believe in or if it was a joke/idiom/whatever