Simpler solution -- provide direct funding to small community credit unions at a low deposit rate, with a stipulation that the money must be used to provide mortgages to first time home buyers within mid-lower income brackets, at discounted mortgage rates.
The CUs win by having direct investment to shore up capital requirements and free marketing to draw people away from the big banks. The gov wins by offloading the task of targeting funds to specific demos on to the CUs, using the gov regulators that're already in place to provide oversight - and by bolstering a 'small business' industry which is also an 'alternative' to the big bank oligopoly. Buyers win by having lower carrying costs/ more realistic price points. Sellers win by having a market of some sort to sell to, which they generally don't at the moment.