Adding more of a slope would be...problematic (lots of work). I've thought of it, and if I did add a slope, I'd probably just go with asphalt shingles, although the options both of you mention are worth looking at.
One corner of the shed is slightly higher than the rest of the shed, it's not a typical peaked-in-the-middle roof. It's also a lot more substantial than your typical shed, we think it was a former blacksmith's shop. Yes, it's that old, perhaps older than the house itself! :P
Cheers,
Mike