Psychocycles

I got into cycling a few years ago and have over the past year been doing structured training at fairly high intensities. Over the past few weeks I have taken that up another notch and am training at race-level intensity. However, I also rock climb & do upper body work in the form of calisthenics (pullups, pushups, etc). I used to workout upper body 3x a week & rock climb 2-3x a week, but since taking up the increased intensity training, I cannot maintain that level of upper body work anymore.

I'm thinking to drop my upper body work to 2x a week & rock climb 1-2x a week to accommodate the increased demands of cycling training but then I have the question of which days to do the upper body work?

I've been listening to the TrainerRoads pod cast and one of the coaches, Chad, is a firm believer in rest on rest days; i.e. no other workouts on rest days. However, rest days are the only days I have enough energy to get in a decent upper body workout. Does anyone else lift/workout upper body and balance that with your cycling training? How do you balance your workouts?