Is it permissible to supplicate that Allah repays on my behalf on the Day of Judgment whatever shortcomings I had in fulfilling people's rights, or whatever harm I inflicted upon them, and that He does not allow them to take anything from my good deeds?

There appears to be no impediment to supplicating that Allah compensate the wronged person from His bounty without taking from the wrongdoer's good deeds if the latter's repentance is sincere. For the completeness of repentance entails restoring rights or seeking absolution from their owners; otherwise, the wrongdoer's good deeds will be taken. If the wrongdoer is unable to restore rights after sincere repentance, it is hoped that Allah will compensate the wronged from His own (bounty) without taking from the wrongdoer's good deeds. Shaykh al-Islam Ibn Taymiyyah mentioned that the repentance of the oppressor does not negate the right of the oppressed. The completeness of repentance is achieved through compensation, and if he does not compensate him in this world, he will be compensated in the Hereafter. The oppressor should then accumulate many good deeds. And if Allah wills to compensate the wronged from Himself, there is no repeller of His bounty.