In the IPG, under Missed Triggers, it says this:

If the triggered ability creates an effect whose duration has already expired or the ability was missed prior to the current phase in the previous player's turn, instruct the players to continue playing.

Does that always refer to the previous turn or would Time Warp enable for example a trigger missed in the previous turn's upkeep to go on the stack in this turn's main phase if both turns were taken by the same player?

It states in the previous player's turn, in this case you are the the previous player so no you could not put the trigger on the stack during your next main phase.