Do you think the number of small council members would have been the same, if there was a Royal Bank, or a royal justice system, or a permanent parliament-like Great Council? Or would they have fallen under the responsibilities of the Master of Coin and Master of Laws? What should an effective small council be composed of, in your opinion?

Well, if there was a royal justice system, you’d just have circuit justices reporting to the Master of Laws who reports to the King. 

If there was a royal Bank, they’d probably report to the Master of Coin. 

But if there’s a Great Council, you’re going to need some sort of Chancellor/Speaker/liaison figure. 

In terms of missing positions: 

1. Master of Agriculture: given the seasons, maximizing agricultural production, minimizing spoilage, and maximizing storage is a national necessity.
2. Master of Roads (and bridges, canals, mills, etc.): Westeros desperately needs improvements to its infrastructure to help drive economic development.