I've had the opposite experience (and posted about it here before). Since I joined Prime last year, I've had issues with the guaranteed 2 day shipping taking 3-4 days or sometimes a week. I don't live in the backwoods either; I'm well within the Atlanta metro area (though not quite inside the perimeter). Before I joined Prime, even a non-Prime eligible item would tend to arrive in 1-2 days.
I did call Amazon about the issue several months ago, and they offered me gift card credit equal to the non-Prime shipping cost of all shipments that didn't meet the guaranteed date, and since then I've only had one late shipment. It definitely pays to contact them about it; I know from working for a company that sells on Amazon that the customer is treated like royalty whenever there's an issue, whether it's with Marketplace or Amazon direct sales.
Instead Amazon has algos that know exactly when they need to get an item in the mail to make it before the deadline. Every time an order comes in, the pickers list is updated.
Meaning that every time a customers order comes in with a tighter deadline, their order will be picked prior to yours, until you deadline is sufficiently close (or there is a lack of more pressing orders) for your items to make it to the top of the list.
Its clearly in their best interest to push people to subscribe to Prime to recover their costs, their order fulfillment is so streamlined that a standard free shipment and a prime shipment probably cost the same in 95% of cases.