CWT Disapointing Frequency Separation
The CWT is not, per se, superior to STFT. Due to its variations in scale, it can be better, for instance, when:


you address natural signals where transients are shorter than more stationary parts,
you do not know the appropriate scale of observation.


which is neither the case from your signal: precise frequency on the same support.

On the one hand, you can work with a continuous wavelet with more oscillations, and better refine the scales and voices. 

On the other hand, there are so-called STFT with windows whose width vary with frequency.

Add-ons like hybrid time-scale/time-frequency transformations, reassignement, etc. may be used, but choosing the appropriate tool requires to refine your goal.