I lived in Denver a Mile High City for 35 years, we lived @ 5600 feet then..... we now live at a higher altitude than that, in Idaho we're nearer to your altitude. I find the comments about butter interesting as I only use butter, not that I dispute them but in my experience butter has never seemed to be an issue for me.
I so agree with Linda's comment earlier...learning to adjust to any type of cooking living at high altitudes, is a hit and miss, trial by error from boiling water, to baking a potato, to roasting meals. Hang in there you'll 'get it' in no time...
As for flour unbleached Gold Medal is my preference so I agree with MarthaT's comment about flour.
When we first moved to Denver from Ohio I had the worst time with baking and I have always loved to bake. An elderly neighbor told me that the 'key' to baking in Denver was to halve the leavening in any baked recipe by 1/2 ... baking soda, baking powder. Once I did that everything cakes, cookies, have always seemed to turn out great for me. I've never adjusted adding flour to boxed cake mixes either, even though I rarely use prepared mixes. I don't adjust the sugar, never used applesauce except to soften my cookies to a more cake like texture.
I have a collection of community cookbooks from all over the US and I just as a matter of habit cut all leavening ingredients in half and rarely have a recipe fail.
I don't dispute the High Altitude chart either... a lot of science no doubt in that chart....but if you want a tried and true seat-of-your-pants adjustment for baking that I was given 40+ years ago....just cut those leavening ingredients in half and see if that works for you.
Oh don't know if this is true at lower altitudes but I know that high pressure systems and low weather pressure systems can really affect baking.
My post is probably all 'junk' science....but 40+ years of high altitude baking I've never had someone turn down one of my cookies! :0)