Carrot Cake Straight Up by jkalman (some of the CC recipes lost their author's name when the feature was updated) is my favorite carrot cake recipe.
Since carrot cake is my DH's fav, I usually bake it in a 13x9x2 so it's easier for him to snack on (no decoration, just cream cheese icing).
I always bake using bake even strips and inverted flower nails (for larger pans or heavy batter) at 325F.
That being said, I think you would still have had problems because of your high altitude, as Narie advised.
Some additional high altitude baking help:
(Start right off by increasing baking temp. by +25 degrees to help set batter.)
High Altitude recipes: