Barry had to load that dart with tranquilizer chemicals, which in and of itself would equal “deliberation.”
There is a frantic event in the backyard, which Barry admits to with the “chipmunk story.”
An expert said that Suzanne would likely be out in a few minutes.
So the theory appears to be that he shoots her, she runs and locks herself in her bedroom, and he breaks in, damaging the door.
Before she succumbs, she is able to scratch Barry on the shoulder with 3 of her nails (he’s probably on top of her strangling or suffocating her at this point).
So the data shows an event, but even if one doesn’t believe it, Barry says it’s true.
A syringe cap is found in the dryer, and darts in the garage. Barry explains that deer somehow come to his garage area, and he shoots them with darts. It’s as improbable as it is illegal, and no antlers are even found.
Taken alone, the physical evidence doesn’t mean much (darts, door, etc), but Barry’s insane stories shape a picture that seems pretty solid to me.