Is it permissible to consider money that was set aside with the intention of Zakat, but did not meet its conditions, as funds for interest-bearing debt to alleviate the burden of debts, instead of considering it as charity?

What you have given in charity with the intention of it being Zakat (definition) is not sufficient to purify yourself from unlawful wealth. You must give away the unlawful money with the intention of disposing of it, based on the Prophet's (peace be upon him) saying: "Indeed, actions are by intentions." Purifying wealth from unlawfulness increases its blessings, it does not diminish them.