>Periodically forgive all debts.

This will be priced into debts, see short term lending rates. Those who can't make money by lending won't lend, meaning the borrowers will have to either not get the money or turn to those who don't play by the legal system.

>I'm curious, but ignorant, of the Quran's notion of riba, the prohibition on interest payments.

The money from interest is instead added to the price. It has some differences (less ability to save money by paying off early), but overall the lenders still make their money.

>I'd like more discussion about our own debt-based economy.

For starters, we can look to stop the sin tax on labor. Granted, most people don't call it a sin tax, but the difference between a sin tax and a tax appears to be marketing.