How do we reconcile God saving His servant by His mercy, not by his deeds, with recompense being of the same kind as the deed, such that the servant sees success and relief because of his righteous عمل (amal - deeds)?

The meaning of the noble verse: (Then when Our command came, We saved Salih and those who believed with him by a mercy from Us, and from the disgrace of that day. Indeed, your Lord is the Powerful, the Exalted in Might) is that Allah saved Salih and the believers by His grace, and from the humiliation, disgrace, and torment of that day; because Allah is Powerful and no one can overcome Him.

Salvation from Allah's punishment and entry into Paradise are by His mercy and grace, and righteous deeds are a means to attain this mercy, not a price for Paradise. This is indicated by the salvation of Yunus (peace be upon him) because of his glorification of Allah, and the story of the Companions of the Cave who supplicated to Allah through their righteous deeds. It is legislated for the believer to rejoice at Allah's granting him success in performing righteous deeds, while realizing that the deed is by Allah's grace and beneficence, and he must not be afflicted with conceit or presume upon Allah with it.