I got the jacks in and realized that they have 6 pins in the back row as opposed to the 3 that the original had.
Here is a link to the exact part if anyone stumbles across this thread and is looking for the part.
If that link does, the search for a 3.5mm 8-pin (the important part) headphone jack, and should cost about $4.50 for 15 pieces. The replacement is really high quality and much sturdier than the flimsy original, but I had to sand a tiny bit out of the case to make it fit. I used a Dremel and then cleaned it with a rounded file.