A couple of years ago, I was exactly where you are now (though with the 2200, not the K3 inks, but it's probably similar). Epson's mantra about drying with paper over it being the "solution" is somewhere between wishful thinking and BS.
After trying a number of different glossy and semigloss papers, I found that they vary tremendously in the amount of outgassing they produce. Epson's are the worst in this regard that I've found. I've found other papers that have minimal outgassing. My current favorite is Ilford Galerie Smooth Gloss. They also make a Smooth Pearl, which is probably reasonably close to a luster finish; I haven't tried it, but I would guess it probably doesn't have much outgassing either. You can get sample packs of that and other papers at inkjetart.com and try them yourself.