Same Account Rolling to Different Parents Depending on Entity

That is not possible because parent Account values do not exist in the database - the values you see in the parent Accounts are dynamically accumulated from the children members. And it is the same for the Flow and UD dimensions but you have more options there because you can set constraints on these dimensions by Entity. I don't think you will be able to get around having multiple parents in whatever dimension you choose and I can't think of way of doing that using the Account dimension.