I appreciated all of your comments on my last post. Thursday morning, which would have been Day 10, it was crystal clear that I needed a rest day and I needed it now. I struck through the word "Run" on my training plan and replaced it with "Rest."
So here is where I am at. I want to achieve 3x week running, 3x week cycling, 2x week swimming plus 1x week rest. The only way this is going to happen is to plan to double up twice a week. For now, I'm aiming to swim+run on Saturdays. If I plan to bike+run one day per week as well, this should all work out.