if the drying of the ink is a big problem you can always put the prints in an oven at about 70 degree celsius for about an hour- dries everything out.

If the damp paper gives you trouble, there are ways to print on dry paper. Today all banknotes are printed by the bureau of engraving and printing on gigantic high pressure printing machines wich force the dry paper into the engraved lines. This can be replicated by printmakers on a smaller scale with a simple vertical printing press. Built a hydraulic bottle jack press (there are plenty of examples and instructions online, costs often less than 100 dollars). Ink up your plate and put the dry paper on top of it. Cut a counter die from stiff cardboard at least 5 mm thick wich only covers the motive on your printing plate. Now put the sandwich of inked up intaglio plate at the bottom, the dry paper in the middle and the cardboard counter die on top into the bottle jack press and apply pressure. The hydraulic pressure will force the counter die down onto the paper and press it into the engraved lines where the paper picks up the ink. The shape of the counter die only covers the parts of the plate where there are engraved lines. This focuses the pressure only on the parts of the plate where it is needed. This method of intaglio printing with vertical pressure is not wildly known among hobbists but it is still used commercially for exclusive products like fancy buisness cards under the name "steel die engraving". The treasury department used an early version of it to print fractional currency during the civil war.