For core, IMO nothing beats Core Advantage. For upper body, IMO nothing beats the gym. I do them both. In the gym, you could do back machine, bench press, straight legged deadlifts (light weight, high reps), dumbell shrugs, cable triceps extensions, Roman chair leg lifts. Don't do pushups: too much strain for you. Go for higher reps on everything to start with, 20-30, then gradually drop to 12, then 8 over a period of months. I do Core Advantage most days, gym twice a week after riding.

Many roadies have neck issues because their backs are rounded. Work on getting your pelvis rotated forward and back straighter.