4 times per week is going to take away from strength gaining. And the intensity of it needs to be dialed WAY down from the examples you gave in both run scenarios. And, if your goal is to bench twice your bodyweight and you only give yourself 5 months of lifting, you will need to allow yourself to put on some bodyfat as a side effect of eating enough to put on the muscle required to lift that much.
Simple is best here. Either Faleev's 5x5 program for those 5 lifting months, or Kingsbury's 5,4,3,10 plan. Remember that your deadlift and squat need to improve to move your bench a lot.
Bmail me and I am happy to share some more details.