Need advice - cycle or strength training before HIM training

Hi.  I've been trying to plan my year and am looking for some advice.

I'm currently training for a Half Marathon in early March.so most of my training is focused on running.  The weather isn't the best for cycling right now but I may get in a ride on the weekend.

I'm planning to do my first HIM in October so my 20-week HIM training program would start in June.

What would you seasoned triathletes recommend I do during the 12 weeks between the completion of the Half Marathon and the start of HIM training?

My options are:

a) Find an aggressive 12-week cycling training program and try to significantly improve my cycling base (i.e. speed).  Less focus on running, but enough to maintain.

b) Focus on strength (P90X or crossfit).  Cycle and run to maintain fitness, but nothing hard core.  Plan on rebuilding running and bike mileage during the HIM training. 

c) any other suggestion

I'm making the assumption that a HIM training program won't significantly improve your run or bike speed.  While there will be some improvement, any significant gains in running or cycling speed need to be realized when building your base before you start the program.  If I'm way off, please tell me.

So, any suggestions?

Ray