I do a significant amount of time in Z2 it is a slow process to get going, A good 6 months at least if your starting from scratch.
The huge plus of Z2 training is it's easy on your body. This means one of your sessions should be short and hard, hill reps one week, intervals something to get your HR through the roof and let your body recover when first starting for a month or so.
You have a great base to start this now so good luck, so with Z2 and speed/strength work you will improve well and stay injury free.