Looking at your method and recipe, a number of factors could be at play here. I have baked many loaves without the butter and cream in an open top bread tin, and have never experienced shrinkage, quite the opposite in fact.
First of all, the dairy components will lead to a much softer "Milk bread" consistency in comparison to a "Traditional" loaf. This will mean the texture is much lighter and more delicate, so when all the steam has evaporated from the bread, as it cools it will naturally shrink as it is not as rigid as traditional bread. Secondly, the bread is partially steamed being inside an enclosed Pullman tin. This will have a major influence on the texture and density as well.
What you want to achieve is for the bread to "Set" as quickly as possible, yet maintaining the delicate soft texture. In a commercial environment, this is done using flour improvers etc. You haven't mentioned how you prepared the dough, hand kneeding and using a food mixer will also have different impacts on the end result. Pre-rise time will also have an affect, as will using a pre-fermented poolish etc. All of these will affect the crumb size and texture to some degree though.
You could try removing the lid 5-10 minutes before taking the bread out the oven to let some of the steam to escape. I'd also be tempted to use full fat milk rather than heavy cream, as this may contributing to the shrinkage.