I lived at 7800 feet for several years and still spend time there. Each recipe seems to respond to different adjustments. What's happening is the cake rises too fast and doesn't have a strong enough structure to support itself. The standard adjustments are"
- Reduce baking powder and/or baking soda
- Reduce sugar
- Increase liquid
- Increase oven temperature
Old advise I never hear anymore is to use more egg. I think the added protein gives the structure more strength. Either use jumbo eggs or an additional large egg. For dense type cakes and brownies, I did well with this.
For lighter styles, I had better luck with reducing the leavening and increasing the oven temperature. Extra egg affects the texture too much.
Start with one adjustment and take notes until you get it right. Here's a good guide with a link to the Colorado State University Extension Resource Center if you need more help
Your recipe looks like it's related to a cake my family makes called Black Joe (because of the coffee I hope) Our recipe uses a whole cup of shortening though (yep that's my family!) and the milk is soured with a bit of vinegar. Nobody ever measured and wrote down the exact amount of baking soda needed. "Just enough to balance out however much vinegar you use."
My Grandma was the only one who had success with it consistently. My Mom still makes it with varying results.