There are different type of rotary encodes some with more than double the cheaper detents per revolution, good luck in finding one that exactly matches the mounting and shaft dimensions.
If you have the time and MCU programming finesse, hack it, put in your own custom controls to set alarm and clock time or to emulate the pulse train output of the existing rotary encode. It only uses two wires to determine direction and "notch."
You can emulate the waveform feeding into the existing MCU. To set, the pulse trains requirements are that the first train of on/off transitions either lead or lag the second sequence of pulses so as to determine direction and "notches."
Just compose your own "acceleration" algorithm to advance by x10 or x20 secs/mins/hrs, etc and determined by speed of rotation by your hand.