How to implement discretized CWT with FFT?
To be honest, if I want to use a CWT, I'll use the toolbox Matlab provides.  

I have every confidence that I could code a CWT, but an efficient, debugged, and tested set of routines is not an interest.

There are a number of open source wavelet codes that a Google search will return, such as 

https://stackoverflow.com/questions/9606458/looking-for-a-good-c-c-wavelet-library-for-signal-processing

so there is code available that you can use and/or modify or just get ideas from.

Also, you haven't posted what you have so far produced, code or equations.  No one can offer any concrete suggestions or advice given your description.