I have the exact same printer with the exact same problem. I tried different paper, different humidity, replaced all kinds of rubber parts, etc. to no avail. I fixed it yesterday by following the link in user3269930's answer. I'm writing the steps here in case the link goes down.
The problem is that one or two solenoids that control the paper feed mechanism are sticking. The foam pads on the solenoids get sticky over time. To fix them, you must disassemble the printer.
- Unplug the printer. Press the power button to attempt to drain the capacitors (can't hurt).
- Remove the front door and paper tray.
- Remove 5 screws and the cover from the power supply on the back.
- Remove the left side of the printer. There are hooks/clips along the bottom, sides, and top. Remove the bottom and sides first, then push up firmly to unclip the top.
- Remove the plastic cover from the fax lines (1 screw and some clips).
- Remove the motherboard (lots of plugs and 4 screws).
- Remove the metal plate the motherboard was mounted on (4 screws).
- Remove the drive unit (6 screws). You can leave it plugged in.
- Remove the triangular, metal plate covering the paper feed gears and solenoids. Maybe take a photo/sketch of the solenoids so you can get them back in correctly.
- Remove the gears and solenoids. You don't have to preserve the rotation of the gears, fortunately.
- Do something about the sticky pads. I applied talcum with a cotton swab. Someone else used electrical tape. I don't know what's best or how long the talcum will work. The solenoids should operate freely without sticking. Be careful not to stretch the springs!
Put it back together in reverse order and you're all set! You can test operation without the side cover on, but you will need to put the front door on. Obviously, don't touch anything that could shock you.