I haven't been able to find any canon references to Muggles working in the Wizarding World, so I'm afraid this is a bit of conjecture and inference, but with the International Statute of Secrecy, it would be highly unlikely. Even though there are instances of Muggles interacting with the magical world as you mentioned, the Statute seems to be extremely limiting.
In Philosopher's Stone, Seamus Finnigan says:
'Me dad's a Muggle. Mam didn't tell him she was a witch 'til after they were married. Bit of a nasty shock for him.'
It's unclear from that if his mother would have been allowed to tell him sooner, but we can take this as a typical example of how a Muggle would normally learn about magic.
The backstory J. K. Rowling wrote for Pottermore goes more into relationships and the Statute. She mentions McGonagall's mother Isobel, before she married, 'had fallen in love with Robert [the boy who would become McGongall's father]. Unfortunately, she had not found the courage to tell him what she was.'
This implies if she only had the courage, she would have been able to, despite them only dating at that point. The backstory later goes on to say:
Isobel explained, through her sobs, that she (and their daughter) were bound by the International Statute of Secrecy, and that they must conceal the truth about themselves, or face the fury of the Ministry of Magic. Robert also quailed at the thought of how the locals - in the main, an austere, straight-laced and conventional breed - would feel about having a witch as their Minister’s wife.
This obviously means hiding the truth from their neighbours, but also their friends, and most likely Robert's family as we know Aunt Marge was deliberately kept in the dark about the Wizarding World. While you could make a solid argument that that was the Dursleys never ever ever wanting her to find out, the fact that the Accidental Magic Reversal Department modified her memory so 'she has no recollection of the incident at all' when Harry used magic on her in Prisoner of Azkaban would suggest the Ministry is against only immediate family - those who actually need to know - knowing.
McGonagall's backstory also plainly states that, when breaking up with her fiance, she would be breaking the Statute if she told him she was a witch; this implies that whomever you tell has to be someone close to you, whom you intend to share the future with. Mother-in-laws might not cut it.
As it's emotional, the timing could be debated on an individual basis - some people get married after a few months, some might not think of living together for a few years - and I'm sure some witches have told close friends and lived to tell the tale, but we can theorise that the understanding is to tell someone you trust enough to keep it to themselves, and only because they have to know.
Fudge's visit to the British Prime Minster in Half-Blood Prince would help back up this theory. He appears in his office just after he is voted in; judging from the British Prime Minister's reaction ('he had been utterly terrified[...] he had remained speechless[...] dumbstruck'), it's fair to say he didn't have a clue about the magical world before then, and we can assume from this scene only the very top people are told. Throughout his entire election campaign, throughout his time working his way up the bench, he had no idea about the Wizarding World.
Fudge tells him:
'I'll only bother you if there's something really serious going on our end, something that's likely to affect the Muggles [...] Otherwise it's live and let live.'
If we take from this that only essential people and immediate family are allowed to know, having Muggles work in the Wizarding World could be seen as dangerous to the Statute, as they would have to be trusted not to discuss their work with their non-magical friends and family, not to ever reveal anything about where they go and what they do every single day. Of course, this is in a world where, twice a year, hundreds of teenagers run at a column in a busy Muggle train station and vanish, so maybe the Ministry don't worry too much about people talking, but given the rules on who can know, who those people tell is likely to be a concern.
But whether the Statute would allow a Muggle to integrate so much into the Wizarding World to have a job, rather than just knowing about it and changing a bit of money at Gringott's, there's a big difference between what the law allows and what people really do.
We know from the books that muggle-baiting is a huge problem, not to mention all the, you know, torture and killing. Muggles are in danger in the Wizarding World. From a business persective, you wouldn't want to hire someone who would:
a) not be qualified for the job. Think about working in a magical pub. You're a non-magical person, and a drunk wizard is accio-ing bottles from behind the bar, or enchanting the taps to flow, or jinxing you so you can't physically move while he helps himself to the night's takings. You couldn't stop him. From an employer's point of view, you would be a massive disadvantage to him, as well as:
b) a political stance that might turn away business and, worse yet, attract a dark, evil crowd to attack your business. Even if your employer was muggle-friendly, he would be running a business which he would want to make profitable. It's not really a big assumption to think that the most powerful and influential wizarding families - the oldest, pureblood families, the Malfoys, the Blacks - are likely to turn their noses at your hiring a muggle, whether they support Big V or not; your employer wouldn't have to be a bad person to not want to lose their business.
But we know the political state of affairs in canon was much darker than that, and he'd be making himself a target to be destroyed by taking such a political stance, too.
You could argue it wouldn't be just any employer taking on a Muggle, it would more likely be your spouse, wanting to work alongside you; but they'd have even more reason to keep you from harm's way.
As with McGonagall and Seamus' parents, the Muggle-Wizard relationships we've seen have had the Wizard sticking on the Muggle's side rather than the Muggle joining the Wizard, and it's likely fair to assume that that's the norm in these cases. Again, a lot of it is likely down to the fact that a Muggle can't do much in the Wizarding World. From a practical point of view, they'd be a bit useless. They wouldn't be able to get into Diagon Alley, hail the Knight Bus, accio anywhere, and they would constantly be a novelty to the magical folk around them. As a Brit who's lived in America I can tell you: that's annoying, guys.
I think, even if there was no legal reason stopping you - though given the Statute and the many departments surrounding Muggles, there could well be - you wouldn't want to live in the Wizarding World and not be a part of it. You would be in danger, you would constantly rely on someone else, small children would have you at their mercy, not to mention the more dangerous folk, and you would feel incompetent. The Squibs we've seen in canon are pretty lonely and a bit bitter, and I think there's good reason for that. You would always be the fool if you couldn't do magic, and no matter how interested you might be in it, you most likely wouldn't choose to live in a world you'd have to be babied in.