Is it obligatory to make up four months of fasting for missed Ramadans in which I deliberately broke the fast due to ignorance of its obligation, especially since I am unable to adequately feed the poor or give charity?

You are obligated to make up the days you missed fasting in previous months. If you are unsure of the exact number, you should make an earnest effort to determine it and fast the number of days that you believe will absolve your responsibility. The expiation for delaying the makeup fast is not binding upon you as long as you were unaware of the impermissibility of delaying it. You must make up the fasts according to your ability, and any days you are unable to make up this year will remain an obligation upon you until you are able to fulfill them. You must repent to Allah and commit to prayer and fasting.