How about try this first, get a florescent yoga mat or something, cut to a bit wider than your bars and stick across the rack?

I had to carry a wheel with 700x50 Big Apple tire home a few weeks back and lashed it on my backpack. Someone commented to me I was being obnoxious carrying something so wide, but they STFU when I told them it's only marginally wider than my 69 cm handle bars.