I do Mark Verstegens Core Performance workouts. Not everyday like the early months, as like you it affected my cycling, but scheduled around my cycling. One thing that may help is a power meter as it will quickly show if you're at the top of your game or whether you probably should have taken a rest day.
His workouts are great. You can move around the system and target what you want. Even if you never did weights his twisting, plyometric type movements, foam roller and stretches (with cycling specific ones thrown in) will help you be better in all sports and help prevent injuries.
I did martial arts daily for years and was constantly injured. After implementing his ideas I don't have anymore injuries in cycling or martial arts. Losing weight had a lot to do with that but so did getting more flexible, stronger core and working the muscles that don't get targeted in my activities. GL