Runners do not need random fatigue. They need strength that protects posture, improves force production, and keeps hips stable when pace starts to drift.
Two short gym sessions per week are usually enough. Focus on split squats, hinges, calf strength, loaded carries, and trunk work you can progress. Keep the lifts honest and repeatable.
The best sign your strength plan is working is not that you feel crushed. It is that you feel more stable, less fragile, and better able to hold your effort on tired legs.
If your club already has a weekly long run, your strength work should support that session, not compete with it.