Is this supposed to be a dense bread? I mixed the dough in the morning and let it sit outside to proof. 12 hours later, I baked it and it's pretty...

Yes, I've only used AP flour for this recipe.

My second batch was better but still not as light as a soft bread should be. I mixed the dough and put it in the fridge overnight, then took it out and shaped it and let it proof at room temperature for 2 hours before baking. It still looked and felt dense. Although it was lighter than the first batch.

Yeast was good. I ran out of butter, so I used coconut oil (1:1 substitution). I even reduced the oatmeal because I thought that was contributing to the heaviness.

I have made these several times and they are not dense - I have never let them rise that long so I think AJ may be correct about over proofing, if you need to leave them for 12 hours I think try proofing in the fridge instead of out to slow it down. They are amazing rolls, I have to be careful not to eat every single one of them when I make them!

They shouldn't be that dense. They're puffy and kind of have the texture of those soft bread rolls that you got in the school cafeteria (only they taste much much better). Maybe your yeast wasn't active?