Is it permissible to go for 'Umrah while burdened with debts that cannot be paid back, or for which permission from the creditors cannot be obtained, even with the intention of repayment?

If the debt is due, it is not permissible to go for 'Umrah except with the permission of the creditor, and he has the right to prevent you, because his right takes precedence. However, if the debt is deferred or you are in financial hardship, it is permissible to travel for 'Umrah even without his permission. It is obligatory to promptly repay the due debt to clear one's liability, as debt takes precedence over Hajj and 'Umrah. If there is no money left after repaying the debt, then wait until Allah enriches you. Financial capability is a condition for the obligation of Hajj and 'Umrah, so if debt conflicts with Hajj, then repaying the debt takes precedence.