Is it permissible to search for a bank to buy out an accumulated, burdensome debt in its entirety, for the purpose of reducing the value of the monthly installments?

It is obligatory for you to repent to Allah for dealing with interest-based banks. As for paying off interest-based debts, it is permissible to deal with an Islamic bank that adheres to Sharia guidelines through tawarruq, by purchasing a commodity from them at an installment price, then selling it and using its proceeds to pay off your debts.