There is no current way RAW to move your turn to a later initiative. The closest you can get is as you described, use your action during your turn to Ready, and take your reaction later in the round.
Per the 5e PHB,
The order of turns is determined at the beginning of a combat encounter, when everyone rolls initiative.
As usual, you can talk to your DM about allowing a Delay in 5e, or maybe "taking a knee" (willingly becoming the last one to take a turn) during the initiative roll.
Per Improvising an Action,
Your character can do things not covered by the actions in this chapter... The only limits to the actions you can attempt are your imagination and your character’s ability scores. ... When you describe an action not detailed elsewhere in the rules, the DM tells you whether that action is possible and what kind of roll you need to make, if any, to determine success or failure.
Alternatively, there is a combat variant in the 5e DMG, page 270, "Side Initiative"
Under this variant, the players roll a d20 for their initiative as a group, or side. [The DM] also roll[s] a d20. ... When it's a side's turn, the members of that side can act in any order they choose.
So while the answer to your question is still no, there is a workaround in the rules.