I don't know details, but muslim banks are prohibited from charging interest and somehow they survive. I would think there would need to be regulations in place to ensure schools didn't suddenly drastically increase prices, and to prevent students from taking far more than they need, but that's doable.
Lowering the required percentage of income for repayment is a good idea too. It would free up more of a young person's income for investment/expenditure, which benefits the overall economy.