Notice the dumpster fire is off limits now?? Leads me to believe that it does have something to do with it after all.
Could this have been the scenario: JI gets home at 2 (not 3 as he has stated). DB is freaking out in her room with a dead baby. "Take it, take it--get rid of it." JI is in shock; "Where"? DB: "to the dumpster at the apartments. Burn it, burn it or we'll both go to jail for life."
JI: "All right. Roams bewildered to dumpster (first sighting of T-shirt man. Eyewitnesses off on the time.) He gets to the dumpster, starts a fire, throws in the baby's clothing, can't let go of the baby. He really loves her. Goes back thru backyard; lays baby Lisa on ground (where dogs got a hit and soil was disturbed.)
DB: "Well, did you do it?" JI: "No, I couldn't."
DB "You f*&^% moron. Do I have to do everything myself? Where is she?"
DB sends him out again. "Do it right this time you da#$% a$$hole!"
JI in T-shirt goes out, wanders 3 miles away still clutching the dead body of his baby girl; gets to the river and throws her in.
He runs home, they go to neighbor and call 9-11. DB has had time to stage the break-in and get her story all together.
...Soon to be a Lifetime Movie.
(The above scenario is strictly the product of a fevered mind.)