There's no reason why you shouldn't use close-up supplemetary lenses on zoom lenses. However, when you think of all that's happening in a zoom lens, when you turn that zoom collar- all those elements moving in relation to each other, it's hardly surprising, that a prime lens tends to be sharper when it comes right down to critical detail.
I'd go the route of a standard 50mm lens. The Canon 50mm 1.8 is a cracking sharp available light lens anyway, is cheap as chips new, and they can be picked up very cheaply on fleabay 2nd hand. This lens would give the option of fittiing supplementary close up lenses in various strengths or getting a cheap set of extension tubes to achieve the same thing. The other option is to get an adaptor ring to mount the lens on your camera in reverse for pretty impressive close-up capability. Remember Bachs's picture of the coin with a reversed lens?
The 50mm lens should be in everyone's bag anyway just for it's low light capabilty.