Of course. That sense of urgency is starting to get on my parents' nerves!
I've got a loose training schedule now. I exercise every day, but my routine is pretty random right now.
Dear HopefulOne,
You are doing well to be thinking of all of this as a junior and it should make a big difference to you attaining your goal. I'm a teacher who acts as our school's advisor to students interested in attending service academies, and I have had a number of conversations with representatives from the various academies, including USMA, in that role. So I hope you won't mind me chipping in with an opinion.
To get back to your original question about whether you really should do a varsity sport: I get that this is not a cost-free decision, given your commitment to your extracurricular and the fact it will somewhat impact your GPA. However, your ACT scores are outstanding. In my experience -- and this is just as an educated observer -- West Point will not regard your academics as a question. They may, however, regard physical activity/prowess as a question for you. Why give them "a question" in any category? If you can do a varsity sport, like track or cross country, you can check that box in your application and help resolve the question of physical stamina/suitability.
As other posters have said, a superb performance on the CFA can help put to rest this issue, but as you recognize (and kudos for your honesty), your starting point for the CFA is significantly sub-par (particularly on pull-ups and the run time). The great thing about the CFA is that it is almost wholly in your control (barring injury): you can improve. But if you are at zero pull-ups and 8 minute mile now, it is a long shot to assume you'll max out with 18 pull-ups and a sub 6-minute mile in 9 months.
If you join a team, you'll help lay the physical activity question to rest; you'll get the points that a varsity letter gives to your application (assuming you can letter); and, perhaps most importantly, you will be working in a structured environment, with expert leadership and guidance and the support of teammates/friends, on improving your physical fitness.
With all that said, you are the applicant -- choose the path that you feel is best for you and be at peace! Good luck to you.