Cross-commissioning is a rarity. Don't rely on the very slight chance that you will be approved to cross-commission. Instead, if you want to commission into the Marine Corps, apply for PLC (Platoon Leaders Course). It is basically a variation of OCC (Officer Candidate Course) but for undergraduates, while OCC is for graduates holding a Bachelor's Degree. PLC, unless you're taking the combined course (which is 10 weeks), is two 6-week courses of selection, evaluation, and training in Quantico, Virginia. The minimum PFT score for acceptance is a 225, the lowest possible first-class PFT score for the Marines. As close to 300 is ideal; a 245+ is considered competitive. Also, you must hit the minimum of 8 pull-ups, 80 crunches, and less than a 24:00 minute 3-mile for officership, which are different minimums than for the regular PFT.
Enrolling in Army ROTC will help indirectly at best. I personally think it's good instruction for maybe, say, drill & ceremony and land nav and perhaps the PT will also help with maintenance, but you're better off saving time and conducting your own PT sessions without waking up every morning at 5 AM. The two PT exams are also very different, each challenging in their own way. You would be better off practicing pull-ups, crunches, and the 3-mile run than attending AROTC PT sessions which focus on raising and maintaining a solid score on the APFT: push-ups, sit-ups, and the 2-mile run, although projected changes for the APFT include a 60-yard shuttle run, 1-minute of rowers, a standing long jump, and changes to the time limit for push-ups and how many miles you have to run. Also, it seems morning AROTC PT sessions are not completely focused on physical training as much as they are focused on attendance, drill and ceremony, typical ROTC stuff... Things like getting in formation, reporting attendance to the cadet platoon sergeant or first sergeant, etc. If PT sessions last only an hour or so, with about 15 or more minutes dedicated to getting in formation and all those formalities, you can bet that by themselves, they won't do you much good in getting close to a 300, let alone for an entirely different PFT. I'd say it's best you save time and the budget for the local university's ROTC department and yourself to focus on academics and conduct your own training sessions which may prove far more effective for yourself, assuming you keep up the regimen. Also keep in mind that many uncontracted cadets are expected to be there not for taking ROTC as an elective, but to eventually be contracted by their 3rd year; it takes up much more of your time than a regular college "elective" class, if you can call it that. Contact a Marine OSO in your local area to let him/her know you're interested in becoming a Marine officer. Best of luck!