WI: The Gowrie Conspiracy succeeded ?

The adult life of James VI and I was punctuated by plots against his person (assassinations or kidnappings) which all failed, most chronologies take the Gunpowder Plot as POD but none deal with the Gowrie Conspiracy, from the 5 August 1600, last plot against the King of Scotland before his ascension to the English throne. It's difficult to know if the fight between the James Stuart and Alexander Ruthven, the Earl of Gowrie's younger brother, was a simple brawl or a real attempt against the king indebted to the Ruthven family, but the two brothers were executed.

Suppose James is killed, what happens next? His eldest son succeeds him on the Scottish throne, at the age of 6, under the name of Henry I of Scotland but who is in charge of him as well as the regency of the kingdom? His mother Anne of Denmark seems the natural choice but James was suspicious of her and refused to hand over the prince to her. How is the estate affected in England, given that Elisabeth Tudor has only three years to live?
 
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