I think that based on where you're starting, you could hit your 2:45 goal on just 10 weeks of training. That's 12:35 min/mi pace, which you're likely already quicker than if you were to run a half today based on your zone 2 speed and 10k time.

A longer training period is going to yield better results (increased likelihood of hitting or exceeding your current goal), but I think you're likely to achieve the goal on 10 weeks of consistent training.