So I just found an individual download for the missing dll file and injected it into the archive of the Winrar file containing GECK.exe.
That's terribly confusing... why are you adding anything to an archive? You should be extracting the archive the GECK comes in into your New Vegas folder, then running GECK.exe from said New Vegas folder.
Instead of the large DirectX installer, you can also use the version that scans what DirectX components you have and just downloads what you're missing:
http://www.microsoft.com/download/en/details.aspx?id=35
Queue