Machine: Windows 8.1

More Research:
I ran the same tests against the other available containers that have BlockStateMeta.

Strange enough, chests, furnaces and hoppers don't need to be updated to set the correct contents of their respective inventory. I can very well read all the content from the ItemMeta and write it back like so

BlockState ret;
Inventory inventory;

try
{
 ret = blockStateMeta.getBlockState();
 if (!(ret instanceof InventoryHolder)) return;
 inventory = ((InventoryHolder)ret).getInventory();
}
catch (Exception e)
{
 // Catch errors such as: throw new IllegalStateException("Missing blockState for " + material);
 return;
}

// Apply
for (ItemStack itemStack : storedInventory)
{
 if (itemStack == null || itemStack.getType() == Material.AIR) continue;
 inventory.addItem(itemStack);
}

// Set
blockStateMeta.setBlockState(ret);

But the other ones (shulkerboxes, brewingstands, droppers) don't update their contents in doing so.

Conclussion:
So instead, please consider the following approach. If the TileEntity is not placed within the world, rather assume that we want to edit it as a BlockState in ItemMeta and store all relevant information not involved in placement. (Such as text of a sign, patterns of the banners, inventories of Containers and so forth.)