Do you think the Small Council still existed during the Regency of Aegon III? Between a SC with up to 7 people + 7 Regents + a Hand (although it seems like the Hand was usually also a regent), that seems like too many cooks in the kitchen. That time was chaotic and we don’t know much about it, but how do you think that hierarchy working? Regents vote and then the SC enacts their will? Is the Hand the chair of the Regents even though he’d ostensibly be beholden to them as a collective “king”?

The Small Council’s responsibilities are probably too pressing to avoid filling those seats, and Unwin Peake had to have some offices to fill with his kin. Oakenfist’s the one person from that era we know had a Small Council position, as Master of Ships, but we don’t know when he was given that title (possibly after his victory against Racallio Ryndoon, but could have been after the regency). 

But yes, too many cooks in the kitchen is kind of the dominant theme of the Regency period. In terms of the hierarchy, it was supposed to go Regents>Hand>Small Council, but quite frequently you had Regents who were Hands, or conflicts between the Hand and the Regents, and lots of turnover, which got the Great Council in the mix, etc..