Here are a couple more fitness standards for mountaineering. Uphill Athlete has an "Alpine Combine," actually in the book "Training for the New Alpinism." The elements are:
1a. Timed 1000 ft vertical ascent on class 2-3 terrain with a pack at 20% of your bodyweight.
1b. If you can't the hike/climb in 1a, do 1,000 ft vertical stepping up and down on a box.
2. Dips in 60 seconds
3. Situps in 60 seconds
4. Pullups in 60 seconds
5. Box jumps in 60 seconds
6. Pushups in 60 seconds.
The book has a table of Poor/Good/Excellent values. However, they say that the exact test doesn't matter, you can make your own. It is more important for tracking progress.
One thing to consider, we actually have a fine place for doing 1a, the Old Rag Ridge trail. If you choose the right starting point you can make it 1,000 ft to the summit, and it will be mostly class 2-3 (the last 1,000 feet is the scrambling part.