After a weeks worth of work I'm proud to announce that I got the Arduino to correctly hook up to the SD card reader. What was the issue you might ask? Well it was simple really, I had a single wire connected incorrectly which I believe was keeping the SD card reader from getting any power. Originally I thought the issue was the the Arduino wasn't connected to the correct chip select pin but it turns out that wasn't the case. It's an odd combination of joy and frustration that you feel when a solution was so simple and right under your nose. Oh well on to the next part.
This was what I had before I fixed the issue.
And here is after, it really is as simple as it looks. Can't believe it was right under my nose.