If you don't like the "bearing in a can" version, check out the RPI-1031 4-direction Tilt Sensor from ROHM, which is more like a bearing in a box. You still might need a few of them to get the result you are looking for, but they are pretty inexpensive. I haven't used them, but I have used the "bearing in a can" and it doesn't take much to beat that.
The RPI-1031 employs the principle of ROHMs advanced photo interrupter technology through the integration of one IR LED and two IR photo transistors. It allows identifying the gravity direction in equipment turning up, down, left and right.
Info at ROHM with nice diagram of how it works:
http://www.rohm.com/eu/highlights/product-news/tilt-sensor-rpi-1031.html
FYI - They are verrrry small SMD parts, and you can find them online for <$5 USD with or without breakout boards.
That being said I still think the mouse wheel encoder would proabably be your best bet. Start looking around for old broken PCs...
willnue