Is this a robust method for analysing correctness of a filtered signal? Is there a more robust method?
Given you can have a "reference waveform" representing the characteristics of your expected signals, to test the "correctness" of the signal extracted from noise use the Normalized Correlation Coefficient. I reference other posts below where I give the details of computing and using the Normalized Correlation Coefficient:

Noise detection

How can I find SNR, PEAQ, and ODG values by comparing two audios?

This will be an interesting approach to compare your different algorithms as the result of removing portions of your signal of interest or keeping noise contributions will both reduce the correlation coefficient as expected; so this will be an excellent approach to accurately indicate which algorithm you use is optimum for your waveform.