Is it permissible for me to receive zakat funds to pay off a debt I incurred due to a loss in my business caused by mismanagement, knowing that my income is sufficient for me and my family, and that paying off the debt will take many years? And in this case, is it incumbent upon me to severely restrict my living expenses?

If you meet the conditions for being one of the heavily indebted (gharimun), then it is permissible for you to receive zakat. A gharim is someone whose debt equals or exceeds their wealth, and they incurred this debt for a necessary or permissible reason. However, if you are appointed as an agent to disburse zakat to a specific person, it is not permissible for you to take it for yourself. If you spend on yourself and your family in a reasonable manner and no money remains to cover the debt, then it is permissible for you to take zakat to pay it off. And if you have some wealth but it is not sufficient for the debt, it is permissible for you to take the deficit from zakat. None of the scholars have obligated the heavily indebted person to restrict their spending in order for zakat to become permissible for them.