It could be that where the MAF is relocated on the new intake's tube is an incorrect distance from the filter, causing the readings to be off. It could also be that the filter is over-oiled (K&N tends to do this when manufacturing to ensure the filter is not under-oiled) and this extra oil is being pulled away by the incoming air, coating the MAF and going through the rest of the intake system as well. So my suggestion would be to buy the cleaning kit, go about the process of cleaning the filter with the spray and a good rinse until the material is greyish-white, let it air dry (which could take a day or two; don't apply any heat because you can damage the fibers, but you can point a fan at it to speed things up) and then re-oil it yourself with the other spray. Follow the instructions for re-oiling that are in the cleaning kit, and understand that you really don't need to spray the filter all that much. You're basically just spraying enough so that the material has a pinkish-to-red color to it, and not so much that it's colored very dark or dripping oil. Spray it, let it sit for a few hours, and then check to see if there are any spots that have lightened up as the oil settles. Touch up those spots, let it sit, and check again. Once you're good, reinstall, clean your MAF properly, and see what happens. If you're still getting your code, I'd put my money on the new intake's relocation of the MAF sensor at an incorrect distance from the filter as what's causing your code.
Another possibility might be to try a high flow style, dry filter similar to the ones K&N makes, only not requiring any oil, and see what happens there. It would kind of stink for that to solve the issue because the K&N filter is a good chunk of what you're paying for with that CAI (because let's face it, a painted and stickered metal tube is still just a metal tube), but the only real possibilities I can see for the issue are too much oil, a bad MAF location, or a combination of the two.
As for the power loss, that's going to happen because the car is trying to protect its engine due to the lean condition it's detecting.
I've used a K&N drop-in filter in my stock intake and had no issues, but I'm always careful not to oil it too much.