(331) Are we really to believe that Heywood did dramatize Shakespeare's Lucrece?

In  1594, the epic poem "Lucrece"  was printed 

with  the name of the dedicating author William Shakespeare .

There is evidence (in  Draytons Poeem " Matilda" 1594, line 36-42 ) that  a tragedy of "The Rape of Lucrece" by Thomas Heywood was acted on the London stage.

 A Print of this  play  does exist from 1608 


                                         

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Are we really to believe that Lucrece, appeared in the same year 1594 as a narrative Poem by William Shakespeare , as a stage Play (tragedy) by  Thomas Heywood, and as a Poem by Michael Drayton? Isn't it more plausible and likely in 1594 (the first year after Marlowe's Life catastrophy) that the author / inventor of the poetic metaphor of the crime of Tarquin versus Lucrece was always the same who published  his (auto) biographic parable as different literary Genres.     Why there isn't a  more consistent explanation  for these strange observations  by Shakespeare experts?                                                        _________________________