I think not training legs because you run and it makes you slow is absolutely ridiculous. Have you seen the thighs on Olympic sprinters or cyclists? They're ****ing massive! Guess what? The both have speed and incredible endurance AND they all train their legs.
Having strong, healthy hips is desirable in any athlete and will further your gains in the gym. I'm not saying do nothing but squat, but just train some effective movements for your lower body. Emphasize on recovery and get some sprints, plyometrics, run if you want still ect
So...I would find a 3 day (meaning 3x a week) full body routine. The increased frequency would be beneficial, though you may not be able to apply as much volume as you would your "one muscle a day" routine. You could also consider and Upper/Lower/Upper/Lower routine.