As far as why not Southampton: at an instinctual level, because I don't believe Cambridge University students would have thought it was a good idea to sneer at one of the great lords of the realm using pointed hints and clues, or mock him for being a fool. However, there are also three important discrepancies that together convince me Gullio could not have been meant to lampoon Southampton.
Discrepancy 1: Mismatch in travel experiences.
Gullio is an army captain who claims to have been at the "University of Padua" in Italy, and to have killed "a Pollonian, a German and a Dutchman, because they would not pledge the health of England." Later, Gullio also claims to have been "at Cosmopolis, at Cadiz, at Portingale voyage, and now very lately in Ireland." However, Ingenioso scoffs in an aside that Gullio had never been any further than Flushing in the Netherlands, "and then he came home sick of the scurveys."
Southampton was a well traveled military man and traveler who had visited the Azores, France, and Ireland by 1600 when The Return From Parnassus Part One is thought to have been written.
Discrepancy 2: Mismatch in marital status.
Gullio is a bachelor. When Ingenioso wonders how Gullio has avoided getting married, Gullio replies: "Nay, I cannot abide to be tied to Cleopatra, if she were alive. It's enough for me to crop virginity."
In contrast, Southampton married Elizabeth Vernon in 1598, who shortly after gave birth to their daughter Penelope.
Discrepancy 3: Mismatch in social status.
Gullio is a foolish social climber who pretends to be on close terms with leading members of the nobility. In one scene he tells Ingenioso, "A countess and two lords expect me today at dinner, they are my very honourable friends, I must not disappoint them." Later, he reports that "The Countess and my lord entertained me very honorably. Indeed they used my advice in some state matters, and I perceived the Earl would fain have thrust one of his daughters upon me..." Ingenioso grumbles to himself, "I think he means to poison me with a lie. Why he is acquainted with never a lord except my Lord Coulton, and for Countesses, he never came in the country where a Countess dwells!"
In contrast, Southampton was at the very pinnacle of the aristocracy, acquainted with all the leading nobles of the court.
as additional arguments against Southampton I should add:
He did not compile a common-place book around 1600.
He was not complimented in an epigram by John Weever in 1599.
He is not known as the author of inconsequential sonnets.
There are no rumors that he was courting a lady to whom he was not married around 1600.