Would the Reformation have had a different outcome if Henry VIII had maintained ties with Rome?
The question is, I think, too hypothetical. For Henry VIII the central problem was the authority of Rome and the Pope, not matters of doctine or worship. Moreover, this was the time when the English monarchy started to chafe at having anyone is any kind of position of power or authority over it. It's often been said that England didn't embrace the Reformation till the reign of Edward VI.
In 1534 Henry the VIII formally initiated the Protestant Reformation. In the short run, The English Reformation allowed Henry VIII to achieve his political goal of controlling the church. In the long run, however, the Reformation brought to England the political and religious turmoil that Henry had hoped to avoid.
How did the working out of the Protestant Reformation from henry viii through charles you provide impetus for english settlement?
Catherine of Aragon did not cause the Reformation. The Reformation had already started in Europe. She however was probably a catalyst for the English Reformation however. If she had been able to give birth to a healthy living male heir then Henry VIII would not have decided to break with the Church of Rome to marry Anne Boleyn.
On HM Queen ELizabeth II's signature... She signs 'Elizabeth R' standing for the Latin 'Elizabeth Regina' ('Regina' meaning Queen). In Henry VIII's case... He would sign 'Henri R' (Henri, before the reformation) or 'Henry R' (after the reformation) the 'R' in this case means 'Rex', 'Rex being the Latin for King'.