Based on your stats I wouldn't be worried about passing BOLC. I saw plenty of guys with slower runs pass IOBC. You're probably about mid-pack of new officers. The only thing that would concern me is the asthma attacks you mentioned. In that environment, falling out of a formation run is generally percieved as a sign of lack of motivation unless there is an obvious injury (i.e. bone protruding through skin). Even a legit asthma attack might be misinterpreted by your TAC. I don't know much about asthma, but I'd make sure you have an inhaler and talk to your cadre when you arrive.
As far as training plans, I think you could make significant progress by using METCONs with a sprint focus and doing one long run per week. This would allow you to at least maintain your strength if not continue to improve. If you really want to excel at the running events, you will need a more running centric program, but this will hurt your strength more. In my experience, crossfit has prepared me much better for combat than endurance running (I was up to 20-30 miles a week pre-CF). The Army is slowly learning this as well, but there are still a lot of leaders out there who think push-ups, sit-ups, and distance running are the pinnacle of fitness training. Depending on your personal goals it may be worth focusing on running in the short term until you are able to max the APFT, but for the long term I would highly recommend using crossfit-style workouts for your METCON instead of distance running.