…in which I’ll catch the conscience of the King.

What, you mean, dear readers, that you are unaware of the Catholic subtext of Hamlet? The theory goes like this: Shakespeare was secretly a recusant Catholic. Under Elizabeth’s strict penal laws he could lose everything by being openly Catholic. For the full and best argument on this read Joseph Pearce’s excellent new book, The Quest for Shakespeare 
The Catholic reading of Shakespeare goes like this: Denmark is a Protestant kingdom taken over by an incestuous, bloodthirsty, lustful usurper. Ditto Shakespearean England. Henry VIII was considered to be the beneficiary of Henry VII’s usurpation of the English throne. He was rumored to be incestuous not only because he married his brother’s wife (as Claudius in Hamlet) but he was also rumored not only to have bedded Ann Bolyn’s sister, but also her mother. The most scurrilous rumor (which can’t be true because of dates) was that Ann was actually Henry’s daughter by Mrs Bolyn. Whatever is the truth, Henry VIII was regarded by his enemies as a violent, incestuous, lustful and bloodthirsty usurper.
That Shakespeare intends Denmark to be shown as a Protestant kingdom is clear because Hamlet and Horatio are students at Wittenburg–the center of Lutheranism.
The decay and anarchy, violence and madness in the kingdom is symptomatic (in Shakespeare’s Catholic worldview) of the anarchy, decay, madness and violence that has descended on England since Henry VIII’s break with the source of moral order, sanity and peace–the Catholic faith. That all ends in bloodshed and tragedy and the collapse of the kingdom was a reflection of the widespread fear within Elizabethan England that the country had departed from God’s will and that the Spanish (read Fortinbras) would invade and sweep through the land.
The play is thus read as a subversive recusant Catholic tract–a piece of subtle propaganda against the Tudor regime. As such it was Shakespeare’s intention that the play (Hamlet) would be the thing that would catch the conscience of the King (or in this case the Queen)
For more on this look up Fr Peter Milward’s excellent writings.
PS: If the work is a coded pro-Catholic work is there any significance in the roles of Rosencrantz and Guildenstern? Rosencrantz means ‘Rosary’ in German and ‘Guildenstern’ means ‘Golden Star’. Here’s a piece that gives a history of the names and suggests they are references to the Blessed Virgin Mary.
 What does it mean? Shakespeare (if he was Catholic) would have been horrified by the destruction and pillage of the ancient Marian shrines of Glastonbury, Walsingham, and many others under Cromwell. The ancient images of the Blessed Mother were taken to London and burnt publicly. In the play Rosencrantz and Guildenstern (representing Mary) are violently killed in England at the orders of Protestant prince Hamlet.