I make this trip every June when I transfer from the Lake Shore Limited at South Station to North Station to take the Downeaster to Maine and when I return to take the Lake Shore Limited at South Station. From South Station you just take the Red Line going towards Alewife to the next stop, Downtown Crossing station, there take the Orange Line going towards Oak Grove and get off at the third stop, North Station and go up to the Amtrak platform at North Station. From North Station you take the Orange Line to going towards Forest Hills and get off at the third stop, Downtown Crossing, and just take the Red Line going towards either Braintree or Mattapan to the next stop, South Station, and you are there.
The advantage is you can enjoy the amenities at South Station and the surrounding area. You also can be among the first to board the Lake Shore Limited. I am going cross country on Amtrak starting on June 15th and I will be making this trip on the Lake Shore Limited to Boston and up to Maine and back the next week June 20th-23rd.
See you on the train and Good Luck!