Try the same climb again, but slow down on the bottom half. On a 6% to 8% grade, you were doing 7 to 8 mph. That's a big effort.

I do better on a familiar climb, since I have a good idea of how steep and long the whole thing is, and can pace my efforts better.

When standing I shift to a harder gear, and slow my cadence way down (on reasonable grades). If I try to keep the same cadence when standing, I'll burn up my legs.

My low gear is 34-29, similar to your low. To recover on an 8% grade, I'll slow down while sitting, and use only light to moderate pedal pressure, enough to keep moving at around 4 mph or so. Experiment with how slow you can go on very steep grades, too--I've gone as slow as 3.1 mph at 35 rpm while standing on a 15-18% grade.

Strava calculates a VAM score on most climbs. That's vertical meters per hour. Your 622 meters/hour, or 2040 feet/hour, is pretty respectable already. VAM is a good way to compare your efforts on different climbs (but very steep climbs tend to get higher scores--any slower, and the rider falls over!)