Thanks to everyone above for the replies. Indeed, I headed down there this morning, and things are looking good.
As stated on their website, they initially refused and insisted they needed 5 days. Once I showed them my itinerary - so not just that I wanted my visa early, but that I needed it - and politely apologized to them several times they acquiesced and promised to return it Monday.
Not a wonderful experience - would've rather done something else with my time - but overall efficient and successful.
This is all subject to edit, of course, depending on if the thing is actually there waiting for me Monday.