Senate Page Program: Summer V.S. Semester

Hello! I am interested in applying for the Senate Page Program but am extremely split on whether to apply for the summer or semester program because each has pros and cons. For context, I would like to go to a T20 University to study international relations or political science.

Here is where I am split: The summer program is shorter (two weeks) and it would allow me to experience the whole thing while not taking up my entire summer and I would get to go back to school as normal. If I was to do the semester program I would get to participate in a Tier 1 activity for five months, make good money, network, and live in the capital. With this, I would be giving up leadership opportunities in Student Council, Clubs, Debate, and Sports. I would possibly be missing out on AP credit chances although the page school is extremely good. I would also be giving up a regional leadership position. For reference, I will be attending a different school this year so I am starting from complete scratch on being elected to things so my only further opportunity would be senior year.

To summarize, my primary question is considering all of this, which program option has the best maximization of looking good to a T20 without hurting the application? All of this is being said assuming I would even get in, but it's extremely competitive so even getting in would be an absolute dream. Would the colleges like a strong internship or many mini-schoolwide and sports-related leadership opportunities?