You seem to have the basics of timing correct, but not the outcome of the situation.
After Dracarys! resolves, along with its associated interrupts and reactions, the next player would indeed have the chance to play an action. It's not that "priority shifts" (in fact, priority doesn't shift in that the FP still has priority for all Interrupts and Reactions) - it's just that it is the next player's turn to trigger an action.
What you seem to be forgetting, though, is that when the STR of Warden's of the Reach is calculated as Dracarys! resolves, it's STR is below 0 so it dies. Since the character dies when Dracarys! resolves, it leaves the table before you ever get to the point of the next player being able to trigger something. Heck - it dies before you ever get to the point of triggering reactions to Dracarys! (since reactions are triggered after whatever they are reacting to resolves).
So no, Tyrell cannot use a STR pump like Margaery after Dracarys! is played if the -4 takes the target character to 0 STR or less because the character dies immediately. There is no delay between resolving Dracarys! and calculating the character's STR, finding it is 0, and killing it. The next player's opportunity to trigger an action comes too late; the character is already dead!
The only way to save from Daracrys! is with a card that both saves and increases the character's STR above 0 as part of the same effect (like Risen from the Sea) - which means it will have to be an Interrupt (since all saves are Interrupts).