I wouldn’t start strength training for rock climbing until you’re redpointing 7a+ (12a) and onsighting 6b+ (11a). The most important thing you can do right now is to improve your movement skills. For a skill-sport like climbing, the technique is way more important than strength, especially at the lower grades.
To compare, if you wanted to learn a backflip, would you focus on getting instruction and learning the technique? Or heavy squats to improve your leg drive? Both gymnastics and climbing have huge strength components, but without technique, the strength is useless.
So for climbing, I would focus on as much easy mileage as possible. Auto-belays are great for this. You could do 2x 20m with 10m rest and focus on precise footwork. Check out the Anderson training book for other drill ideas.
For endurance, don’t wait until 16 weeks out. Start now. 16 weeks is the bare minimum to see any appreciable gains in aerobic capacity. You can never have too much base, so the more easy training you can get in between now and your trip, the better off you’ll be.