Is it permissible to consider the additional amount paid in the second debt as a payment towards part of the first debt, especially since the additional amount is less than the first debt?

What we understand is that the person returned the money to fulfill the second debt, not the first. If your first debt is due and legally established, and he is solvent enough to pay it, then there is no impediment to holding onto the amount as part of your debt. However, you must inform its owner to clear his conscience of this portion, so he does not demand it thereafter. Al-Bukhari said: "Chapter: Retribution for the wronged person if he finds the property of his oppressor." Ibn Sirin said: "He may retaliate against him," and he recited: ﴿AND IF YOU PUNISH [AN ENEMY], PUNISH WITH AN EQUIVALENT OF THAT WITH WHICH YOU WERE HARMED﴾ [An-Nahl: 126].