I like this thought process.If you ride a fixed gear, you have a built-in excuse for walking up hills. I usually wait until I'm struggling up at 5 kmh or slower (about 3 mph). I can walk at 5 kmh, so I'm not losing time by walking. At the Knoxville Double last year, it was hot and I was cramping, and Loch Lomond has at least a 15% grade (my limit for the 44x17), so I got off and walked over to the shady side of the rode and pushed the bike. And I was keeping up with the guys still riding.
In fact, I think that if you are riding slower on a geared bike than you would be if you were walking, then why ride? Pride at not having to get off and walk? But you've got guys walking up faster! This is why I've never liked having super low gears on a bike (unless it's a tandem, where you need the super low gears and the triple chainring). If your rear cog is bigger than the front chainring, you are seriously undergeared, and you will be riding slower than a walking pace! Relax, just get off and push the bike! Even the pro's will run with the bike (check out any of the Belgian races over the cobbled climbs).