Step 2 is flawed logic. Make excess principal payments on your highest interest rate loans first. This will result in the fastest paydown of outstanding debt as it will reduce interest costs.
I live in Massachusetts, where property cost is really high (a shoebox house in the worst part of town is at least $250,000). No bank expects 20% down, let alone 15%. If you can do that, awesome. Banks around here like at least 5% down. I would put 20% of your check into savings each pay period, and after two years I would get a 3 year CD with a high interest rate. Your credit score is fine and as long as you keep doing what you're doing with bill payments. Keep your debt to income ratio low and you will be good. 5 years for a person of your age with a graduate degree sounds like a long time to save for a down payment, but I don't know your circumstances.