I think you are simply over doing it. You must pace yourself for anything more then a short climb. I have a rather steep hill with soft gravel and loose stone I like to climb using 21 gear inches. I learned very quickly the importance of pacing myself if I want to make it to the top.
As a recreational cyclist my cadence is in the 63 - 72 rpm range for cruising. Perhaps 80 rpm for short power a burst. I think you're cadence for climbing is WAY too high. I don't know the mechanics involved but it seems easier to climb for a few minutes at a lower cadence even though on a flat, a higher cadence seems to be best, at least for me.
I'd practice at a much lower cadence in a higher gear for starters to build leg strength, and work on pacing your self.
Last edited by xroadcharlie; 03-28-20 at 08:41 AM.