>The carrots take up quite a bit of space in your stomach, and I would wager their GI is far below breads/etc., so I would expect that I'd run out of space in my stomach before their GI became something to worry about.

You're on the right track, but what you mean is not the GI of carrots is low, but the glycemic load. For blood sugar and diet considerations, the GL is at least as important as the GI

http://www.health.harvard.edu/diseases-and-conditions/glycem...