my buttermilk pumpkin cake is so dense & moist that it's like peanut butter! (do not like)
I know this might be a real no no for serious bakers, but you can add a 1/2 cup of pumpkin to a white cake mix (add spice if you like) and top with a homemade cream cheese frosting and it will set a crowd on fire. It is really good for chocolate cake mixes too.
The cake mix I add eggs, water and oil like normal.
My first thought is to add more flour. Sounds like you have too many moist ingredients. Also maybe reduce the oil a bit. Martha has a notoriously heavy hand with fat.
Adding egg and milk would seem to increase, not decrease the moisture. Also, maybe you could spread out your pumpkin puree on a baking sheet and bake it over low heat to remove some of the moisture before incorporating it into your bread.
Last idea: bake longer, and use a little more leavening to make it fluffier.
Best to repost the recipe, or to link to it so we can see specific proportions - you have a few moist ingredients in there and my guess is that the measures are off somehow (or need to be tweaked to your liking). Also, are you sure you baked it long enough? Can be a tricky thing to judge, sometimes, when baking w/pumpkin.