This is for an internally developed printhead test tool (at hp) so money is not as much of an issue. We place the paper on a very flat vacuum platen and then print various test patterns with our (industrial) printheads. So the printing part is easier than what you're doing, printing more or less the same way you'd do in a flat-bed plotter.

We did play around with various ways of picking paper and it's generally a tricky problem, even now we have to adjust the flow for different paper weights. We also came up with a simple way of dropping off extra sheets by forcing a little bow to the paper and shaking a few times for the extras to fall off.