Update: I have since tried the last suggested combination of 66 kOhms (couldn't find 62k at Radioshack, so had to put two 33k resistors in series) and 0.1uF components. There is no change whatsoever; I still see the output signal go from 5V to 0V in response to duty cycles from 100% to 50%. The output stays zero between 50% and 0%.
Thanks for continuing to provide input. Hopefully, this issue gets resolved soon.