Capturing installed applications with MDT
Solution 1:
I figured out my own problem.
I had forgotten to import the captured image from the \Captures folder into the \Operating Systems folder. Once that was done I had to modify the Install Image contained in the Task Sequence under "Install"->"Install Operating System"->"Operating system to install" to point at the captured .wim file.
Someone else also taught me that MDT is typically done in a more hierarchical manner than what I am attempting. What I am trying to do is basically deploy a barebones image, modify that image, and rewrite the original barebones image with the modified one all on the same deployment share.
What I should be doing instead is creating a barebones deployment image on a deployment share. Then modify the barebones image and capture it under a new deployment share.