Perhaps I should have been balancing my weight at the 3 and 9 o'clock positions?
Bad idea, if you mean unclipping one foot at either the 3 or 9 o'clock position while standing and coasting. As soon as you do that, the clipped-in foot will rotate down forcefully to the 6 o'clock position. If this rotation comes unexpectedly, you might lose some control.
As to unclipping at 6 o'clock while standing and coasting: I applaud your courage, but there's no control over the bike as soon as you unclip. It basically amounts to a jumping-off the bike and hoping for the best.
Bottom line: learn to unclip the 12 o'clock foot while standing and coasting. Many riders find this to be a relaxing and safe way to roll up to an anticipated stop. You might find it a bit less awkward if you lean forward over the bars as you unclip.
Last thought: for brief periods, you can sit on the top tube while pedaling and / or unclipping. Don't cram the top tube into your crotch, though. Rotate your body left or right a bit and put your left or right hamstring muscle on the top tube. It approximates seated riding and would have come in handy during your predicament.