The lifting isn't really useful (like others have said) for climbing. I did no squats or dead lifts and in 18 months increased my FTP from 220W to 300W. Any time you spent lifting could probably better be spent just riding your bike.
Train to suffer more. This applies during your rides and just riding in general. Many of us (and we're not pros) can handle 10 hours a week/5 days a week of riding. We aren't genetically more gifted than you. I think many of us accept we'll be fatigued to some degree but also manage our fatigue so we aren't over-trained. Training will also allow you to pace yourself better and know what your limits are so you can go right up to them on climbs. It isn't all about simply being fitter, it's about almost-but-not-quite blowing up and keeping going. Embrace suffering. Suffering isn't bad, it just means something good might happen.
Ride more. My riding fitness is much higher simply going from 4-6 hours like you to 10 hours per week. And that extra time is almost entirely in Z1 or Z2. Just making more mitochondria so I can feed more energy to my muscles before I hit my lactate threshold. It was truly shocking how much fitness I gained (and weight lost since I had a lot to lose) simply by riding in Z1 and Z2. It never feels like you're working really hard and then, boom, you're dropping people on climbs.