How do you plan to show up on time if one of your meetings ends at 2pm, the next one starts at 2pm, the meeting rooms are 3 floors apart, and you need to go to the restroom because you've been in meetings since lunch and need to pee? You're going to clone yourself?
You have to reject one meeting invitation and tell them why.
Isn't the easier solution to stop meetings 5 minutes to the next meeting slot?
At the start of the first meeting, you annouce that you need to leave at 1:50 and ask the meeting to respect that.
1:55 pm “I gotta run to my next meeting” and slip out the door.
Tell the people in the first meeting at the start that you’ll need to leave a few minutes early, to set the expectation and make sure any important stuff is done early. Then when it hits your transition window, politely tell them you have to run and leave.