Try to go to the immigration before your visa expired a couple days before, if they refused to give you the Covid extension, they will give you 7 days to leave the country. And that 7 days will help you to extend your stay until your flight. Is this a good plan?
I think what the officer mean is if you want it quick you have to pay them extra money. Let's see if they will give you a receipt or not, if not then it's under the table. They can't take your passport away for 2 weeks, you are supposed to have your passport with you at all times. I think they mean they will give you the "under consideration" stamp and have you come back after 2 weeks to get the result if they will extend it for you or not. The extra money is just for them to make it faster for you.