How about appealing the decision? I haven't done any formal science in 12 years (we can opt out at 16 in the UK) and they let me in the 2 year program. I don't know how you did in the science portion of the NLN, but if you did well, they should consider it.
Also you have some leverage, as you can say, well LICHSON offered me the 2 year. Maybe offer to do some science courses in the summer? They seem pretty good at PBISN at accommodating you, and working with you, so it may be worth a shot!