My 2 cents:
Sure, try transferring if Stanford is where you would most like to be, but there is no need to spend 200 hours on your transfer application or put most of your energy into the transfer process. As you and I know, nothing is guaranteed when it comes to admissions to these top schools. Attend HYP, do well, get a great GPA, and get to know your professors who you can ask to write recs. However, if you don’t get into Stanford, embrace your current (amazing) school. Maybe you can go to Stanford for grad school. Or maybe you will fall in love with your current school. Take it day-by-day and enjoy the journey!