As you surmise, you have more than adequate general strength. You just do not need to be super strong for climbing (except, as you note, in the climbing specific muscle groups). I certainly do no know many climbers, skiers or runner who can deadlift even 2x BW. Spending time trying to get stronger in that non-specific way will be a waste of your time. You should spend you time developing sport specific strength and the muscular endurance that can stand on top of that specific strength. Devote your strength training time to finger and core strength and doing climbing specific workouts.
Doing a bit of general strength maintenance, as you note will be good for injury prevention. Stoping heavy lifting may help you loose some muscle mass in your legs which will probably pay off in climbing performance too.