Not SQF, but I'd definitely give the "new" product a traceability code of its own.
In terms of identifying the history of a batch, the original code links you through to the raw material and the processing involved in e.g. making the whole peeled potatoes.
When you reprocess these you are further changing the material, so having a unique code for the resulting product allows you to differentiate it from the original "finished" product that subsequently became the raw material.
It might be possible to have your own systems set up to not require this, but I do think it makes it much clearer and therefore would always prefer it as an approach.
Not familiar with the SQF guidance, but in general "recouping" is concerned with getting something back that was, or would otherwise be, lost. In the example you gave of the whole potato / French fries, the latter allows you to recoup (get back, or realise) the value of the whole potato that would otherwise be lost if you'd had to just dispose of them.