Well about a year ago the Canadian and UAE governments had a bit of a falling out. Emirates Airlines wanted more landing rights at Canadian airports but weren't granted them, so the UAE kicked the Canadian military off a base they were using. All rather petty diplomatic stuff. But it meant they cancelled a prior visa waiver. So the bad news for you is that whilst a couple years ago you would have got a free 30-day visa at the airport, now you have to pay quite a sum.
I'm surprised the UAE embassy in Korea can't get you a visa. (Isn't that their job?) Might want to try contacting them again, preferably ring/go in person. If that fails, then perhaps ask the Canadian embassy what they recommend.
I know Emirates and Etihad airlines do cheaper visas through their websites when you fly with them, might be worth a look.
I'm pretty sure a transit visa is only 96 hours. Overstaying is risky. As with border control anywhere in the world, whether they give you a massive fine and lots of hassle or just a (verbal) slap on the wrist is entirely dependent on their mood. Don't suggest you mess with them though!