Here's what Robert Charles Anderson says in Great Migration Begins (p 900):
"In the 1623 Plymouth land division, William Heard was granted one acre as a passenger of the Anne in 1623 [PCR 12:6]. As he does not appear in the 1627 land division, he must have died or departed soon."
Note that no reference is made to him being a signator of the Mayflower compact.
Thanks Jillian - Got that on the Mayflower compact - had some references but not on the official lists. Other than that, he remains a complete mystery.