"Having a new design in hand, Jaques turned to his brother-in-law and entrepreneur, Nathaniel Cook, for advice."
This is not quite correct. In fact, Nat Cook married into the Jaques family later.
As Cook was Staunton's editor (Staunton had a regular chess column) at the ILN during the period leading up to the launch of the set and after we can be reasonably sure that it was largely Cooks design. Cook was setting Staunton's positions in the paper and of course, was well used to the already established book icons, on which the pieces are modelled.
Staunton did once claim to be the designer of the set bearing his name in one column (In the ILN) but only as referencing a correspondent and one can assume if he had, in fact, had anything much to do with it he would have said much more to that effect.
His reference to the so-called Edinburgh pattern as being designed by a 'Lord John Hay a few years previously' is not born out from any other source. The Edinburgh chess club site has little to say on this point (last time I looked).
The popularity of the French Regence set design on the continent was the main contender but was really not suitable for club play, the pieces often being similar (pawns, bishops queens etc).
There was a Spanish design by a famous artist which made a brief claim to fame but wasn't really in the running for long.
Cameratta made up most of what he claims on the HOS site from whole cloth and his worde must be read with caution.
Az, he isn't going to hear you. What is clear is that stationmaster is unable to engage with what other people say, believes that everyone else is some kind of shill for evil fake chess set sellers and that its his job to go on ad nauseam trying to rescue innocents from bad guys who don't sell through ebay (which is pretty much everyone else on this site) and doesn't care or can't tell whether what he says is either true or internally consistent. Thats not a scenario that is going to be influenced either by rational engagement or shouting. We aren't dealing with a member of society here.