I can speak from experience having been injured a few times that biking is not a good exercise to make up for a large volume of training if you have alpine goals. If I’m injured and have to bike for a few weeks, I’m noticeably worse off when I get back to full training. I also live in a flat area. You should focus on running/hiking/stairs as it’s most related to the sport. If you don’t have the mental fortitude to just crank down and go on long runs, I doubt your chances of success with large alpine goals. Sorry to be the bearer of bad news. As someone who used to hate running, I’m betting that you don’t like running because you aren’t good at it, and that is easy to change.
Otherwise on calculations, you’re pretty high on starting values if your fitness is poor. Your weekly volume should be further down around 4 hours, not 8. Since I don’t know your background, I would structure a low end plan somewhere along the lines of 1h/30m/30m, a base strength day, and a day or two of climbing work… or something like that, depending on your goals. I would do the 1h and one of the 30s at Z2, and one of them at recovery (Z1). Then every week increase your aerobic times. Think long term with your goals; overtraining and over use injuries are a big setback.