Did Marlowe Die in Italy?

I have been planning this trip for several years. I want to write a screenplay about Christopher Marlowe, with the premise that he wrote the Shakespeare plays as an ex-pat living in Italy.

See the Front Line PBS production: "Much Ado About Something" in 2003.
http://www.pbs.org/wgbh/pages/frontline/shows/muchado/

In the transcript from PBS, John Hunt is quoted as saying  "The evidence is in the form of notes which Mr. Hoffman, aged 75, received this year from the will of a journalist friend. These say that a 16th century Paduan, Petro Basconi, left papers stating that an English writer named Marlowe lived with him as a recluse until dying in 1627, 11 years after Shakespeare's death.The notes add that the writer had had to leave England. The papers were passed down the Basconi family and were said to have been shown during the 19th century to a British ambassador to Italy, who is said to have commented that he was afraid to tamper with a matter so dear to the English heart."