... The only way I think it could be done and stay close to true is to have dream sequences that Aragorn has flashing back.
Perhaps here the scene in "Many Partings" near the Gates of Moria, where Gandalf, the Hobbits, and Elrond, Galadriel and Celeborn with their respective retinues stay for seven days before the Lórien group head off towards the Redhorn Gate and the Dimrill Stair:
"Often long after the hobbits were wrapped in sleep they would sit together under the stars, recalling the ages that were gone and all their joys and labors in the world, or holding council, concerning the days to come. If any wanderer had chanced to pass, little would he have seen or heard, and it would have seemed to him only that he saw grey figures, carved in stone, memorials of forgotten things now lost in unpeopled lands. For they did not move or speak with mouth, looking from mind to mind; and only their shining eyes stirred and kindled as their thoughts went to and fro.
That Arwen also has this ability seem clear to me. Aragorn is of course separated from his uncle Elrond by 64 human generations following Elros. But Aragorn is also seen as something of a throwback to the old kings of Númenor (much the same is said of Denethor on a lower plane, him being less mingled than others), so perhaps more of such an ability resides within him. I mean, wrenching the Orthanc Palantir from Sauron's control makes Aragorn superior to Saruman the Maia in this respect (that Palantir scene is another one PJ blew sky-high: dude, Aragorn kicks Sauron's butt, not the other way around!!!)
And last, in TA 2980, Arwen and Aragorn plight their troth on Cerin Amroth in Lórien, a "'til death do us part" pledge of the most serious sort. Aragorn was 49 by then, and it had been 29 years since their first meeting, and Aragorn had been places, nasty ones among them, for the preceding 23 years. He had also met and befriended Gandalf, and had served in disguise both kings Thengel of Rohan and Ecthelion II of Gondor. So though probably the abilities mentioned above were far stronger in Arwen, their intense bond could have made some sort of communication at a distance possible. Perhaps the "dream-sequences" as shown in the movie are not that far off the mark - but they would certainly not be Aragorn's internal dreams in my scenario, but the link that exists between Arwen and himself, just not possible during waking.