lord of the rings - Why could Elrond not delay his one-way voyage to Valinor for a few more years?

There are a number of false assumptions in this question.

Firstly, there was no requirement for the children of Elrond to make their choice at the time Elrond leaves. Letter 153 explicitly states that the sons of Elrond did not do so:

The end of his sons, Elladan and Elrohir, is not told: they delay their choice, and remain for a while.

Secondly, Arwen's choice was actually made long before Elrond's departure. Appendix A, the Tale of Aragorn and Arwen, places this event during Aragorn's visit to Lórien after his long journeys East and South (Third Age 2980):

And she stood then as still as a white tree, looking into the West, and at last she said: "I will cleave to you, Dunadan, and turn from the Twilight. Yet there lies the land of my people and the long home of all my kin." She loved her father dearly.

When Elrond learned the choice of his daughter, he was silent, though his heart was grieved and found the doom long feared none the easier to endure.

Having thus already made her choice, Elrond could have waited a few years (which he actually did: there were 3 years between Aragorn's marriage to Arwen and Elrond's departure) or he could have waited a few hundred; it wouldn't have mattered because the parting between Elrond and Arwen was a parting beyond the end of the world:

The Third Age ended thus in victory and hope; and yet grievous among the sorrows of that Age was the parting of Elrond and Arwen, for they were sundered by the Sea and by a doom beyond the end of the world. When the Great Ring was unmade and the Three were shorn of their power, then Elrond grew weary at last and forsook Middle-earth, never to return. But Arwen became as a mortal woman, and yet it was not her lot to die until all that she had gained was lost.

So Arwen had no option at all to "have her cake and eat it", as you put it. She had already made her decision in TA 2980, she married Aragorn in TA 3019, whereas Elrond didn't leave Middle-earth until TA 3021. That dates Arwen's choice to 41 years before Elrond's departure.