Instead, can’t I get similar body movements from the Killer Core and Strength Training (that I’m already doing) and drop the indoor gym? Alternatively, can I get another UA plan that will be a good substitute for indoor climbing gym?
No, absolutely not.
Rock climbing is a complex technique sport (like gymnastics or martial arts) where strength is an important but secondary (perhaps tertiary) component. You will not be able to fitness your way to better rock climbing. You need to practice movement skills.
In addition to a climbing gym, the Anderson book will give you a solid foundation in training fitness and practicing technique. I can’t say this enough: DO NOT neglect the latter.
I’m interested in mountaineering and alpinism and do rock climbing for those objectives.
The degree to which you need technical skills will depend on your goal climbs. If your goal events are primarily general mountaineering, then you may need little to no technical movement skills. You’ll need both fitness and technique for technical alpinism.