Well after Prometheus but a long time before Alien Covenants announcement....
Ridley said that David and Shaw are going to the planet of the Engineers, what they find are not Gods or a Benevolent Race but that David is bringing Hell with him (Cargo) and what happens if the Black Goo is used on GOD? or Machine?
If they have not changed this idea since... then indeed David and Shaw are heading to Paradise in that Ship (he confirmed this when talking about Alien Covenant) and his previous comments hint the Ship does have Bio-Weapons on board.
Ridley had not confirmed that for AC but that indeed the Juggernaught they left LV-223 on does arrive at Paradise.
This does not rule out that it had Deadly Cargo.. we can only assume it would.
As for leaving LV-223.... i think David can Navigate the Ship to where ever and if it was set for Earth he could override it.
The Weyland Viral Sites hinted the company knew a bit about LV-426 and that David was given some knowledge too prior to the Prometheus mission and only he knew about the signal from LV-426.
If this Viral information is to be considered Canon... then indeed combined with what David saw in Prometheus and what he may have read from Engineer Writing etc...
Maybe he decided to go to LV-426 first? But if that signal was similar to Shaws SOS for Earth.... Then David would maybe know that only Death lies there.
David knows the Gods are Mortal, the Engineers only as powerful as the knowledge, technology and tools they possessed.
If they came from Paradise.. David may think that more rewards are there and so he headed right for Paradise.