Q: Regarding dispensational resurrection, what does it mean when it refers to sleeping souls?
A: The quote that you referenced is from a section titled The Dispensational Resurrection, which describes the mass resurrection that took place following Jesus' resurrection from the tomb. The specific quote is here:
When Gabriel referred to "the dead of a Urantia dispensation, " he was referring to these very souls who were now being resurrected—those who had died, but who had been asleep since the days of Adam—a long time for some of them—over 35, 000 years. When some people die, they are not resurrected in three days' time, but instead, they stay peacefully asleep, awaiting just such a time as this one described, a dispensational resurrection, in order to move forward.
The circuit of the archangels then operated for the first time from Urantia. Gabriel and the archangel hosts moved to the place of the spiritual polarity of the planet; and when Gabriel gave the signal, there flashed to the first of the system mansion worlds the voice of Gabriel, saying: "By the mandate of Michael, let the dead of a Urantia dispensation rise!" Then all the survivors of the human races of Urantia who had fallen asleep since the days of Adam, and who had not already gone on to judgment, appeared in the resurrection halls of mansonia in readiness for morontia investiture. p2024:4 (189:3.2)
You can read more about sleeping survivors HERE
Whether a person was resurrected in three days, or whether they may sleep for thousands of years, they still eventually are resurrected on Mansonia, there to begin their "real life, the ascending life."
As for "judgment, " here are a couple of quotes from Jesus:
I am not aware of any place in The Urantia Book that describes an actual process by which mortals are judged. Perhaps the judgment is inherent in the fact of survival itself. The Urantia Book says that we gain nothing from resurrection, save the experience of survival..
"... Do you not perceive that, when each of you is called to lay down his life struggle and pass through the portal of death, you stand in the immediate presence of judgment, and that you are face to face with the facts of a new dispensation of service in the eternal plan of the infinite Father? What the whole world must face as a literal fact at the end of an age, you, as individuals, must each most certainly face as a personal experience when you reach the end of your natural life and thereby pass on to be confronted with the conditions and demands inherent in the next revelation of the eternal progression of the Father's kingdom." p1915:4(176:2.7)
"Mankind can appropriately be divided into many classes in accordance with differing qualifications, as they may be viewed physically, mentally, socially, vocationally, or morally, but as these different classes of mortals appear before the judgment bar of God, they stand on an equal footing; God is truly no respecter of persons." p1468:3 (133:0.3)
It could be that your idea of this mortal life being itself a "judgment, " is on the right track. One can, in this life, decide to survive. One can have only a "faint flicker of faith" in such a resurrection, and we are told that this is the only requirement for survival after death. "All who will may come."
There may possibly be circumstances where a resurrected mortal may be in conflict about survival, or perhaps their dedication is lacking, or for some other reason, their life is reviewed and judgment is made as to whether they are fit to continue. But I would imagine that the majority of mortals are adjudged to be "fit, " to survive the death experience.
We have such a limited understanding of the meaning of life and what's in store for us during the Paradise adventure while we're here that it seems unlikely that we are able to make a knowledgeable decision whether to continue or not, so that decision will most likely occur on the mansion worlds. But, if during this earth life, the person has not exhibited even the smallest flicker of faith and has not produced a soul that can be resurrected then there is no "person" to be resurrected and their existence would cease at mortal death.
Thanks for this really good question ...