You can get accelerometers sensitive enough to make a digital electronic spirit level.Yet the elevator arrives at some velocity after not moving, therefore it must experience acceleration in addition to the static acceleration of the of the earth's gravity.
In theory this can be done with a sensitive enough accelerometer. Would you mind describing your accelerometer experiment? Somebody might be able to make a helpful suggestion.
The ultrasonic option could well be impaired by the noises from the machinery, optical sensors probably wouldn't be reliable because elevator shafts tend to be dirty environments.
For position sensing on the cable drum, Hall effect sensors might be the best option.
One opto that hasn't been mentioned - the opto-gyro which I think was used for navigation when they dug the channel tunnel.
As far as I can understand it - laser pulses are sent round a big reel of fibre-optic cable. The speed of light is a constant (for that fibre-optic medium) so rotating the drum will advance or delay the pulses that emerge from the other end.