Should I expect a size smaller than 1.3 GB from a 15-minute video? Yes
1MB per minute is reasonable for screencasts.
If you look at recommended youtube video sizes, one option is 854x480 For a video of that resoultion, with H264video compression and AAC audio, we get 1MB per minute.
If so, what kinds of things can I look at or what kind of workflow can I engage in order to achieve a more optimal size?
Your work-flow looks correct, you just want to compress the result further at the end. I use camtasia, there are free alternatives, easy h 264 perhaps. If you're really stuck, upload your video to youtube and let them take care of it.