Is it permissible to take out an interest-bearing loan to pay off multiple debts, knowing that there is no other way to pay them off and that failure to pay will result in material and moral harm?

It is not permissible to borrow with interest (riba) except in cases of necessity that permit the forbidden, such as when one cannot find what sustains life, or to avoid imprisonment. In such a case, it is permitted to the extent of the necessity. It should be noted that borrowing might increase the harm in the long run.