Conventional wisdom is that killers move victims in order to get them to a place where they are safer in carrying out their crimes. That's why people are advised to fight to stay where they are if someone tries to abduct them. When kidnappers want to move a victim, they have a reason (although we may not full understand that reason. There are hundreds, maybe thousands, of victims who were abducted and then killed elsewhere, just as there are victims killed in the home.
I just watched a video series on shocking serial killings near Pittsburgh in the late 1970s, in which a man did home invasions, killing the husband, usually by shotgun, and then abducting the wife. Here you have someone willing to kill in the home (and using that to gain cooperation) but who wanted to remove the women from the home to carry out the next phase of his crimes. In the one case where the crime was interrupted, and the wife survived, the killer nearly beat the woman to death because she resisted leaving the home. He left the children in the home, unharmed. He committed planned killings, selected according to his own psychological needs (single story home of married couples) , random crimes of opportunity, and one known killing where he apparently "settled" for a victim outside his pattern. One killing of a couple was of a pair of teenagers in a car at a lover's lane, where the location differed but the rest of the pattern held.
Here is a link to the video segment in which law enforcement discusses the psychology of this killer.
In the case of the Rogers family, the killer planned a ruse to get the vacationing Rogers women onto his boat, voluntarily. The killer has also been linked to another murder by DNA. In this case, he slashed a woman's tires while she was at work and kidnapper her at that point. So some of the behavior (identifying victims, planning a scenario) was the same, but the scenarios differed. In the Rogers murders, the killer tried to dispose of the bodies in the ocean while he left the body of the other known victim in a place where she was found. So we see that even among known serial killers, there is a range of behaviors.
My point, I guess, is that we can't start with what either the perpetrator or victims in this case thought or believed. We have to look at what we know, the evidence we have. We know that this starts as a kidnapping. We know that the kidnappers didn't want to carry out their full crime against the women in the Levitt home--or that would be the only crime scene. There are many, many home invasion killings (see above). We know that either the women were removed from that home or taken as a group while out of the building (e.g., they were outside for some reason before the abduction or elsewhere, e.g., George's Steakhouse theory). We know that the vehicles remained with the home, along with the purses and other items significant to the women (money, shoes) and so it is most likely that the house is the first crime scene. The only other alternative is that kidnappers returned to the house after abducting the women and returned those purses, which is theoretically possible but not plausible.
We have actual evidence that they were taken from the home, including Stacy's shoes and clothes, the wet washcloths indicating the girls were getting ready for bed, the purses, the trace of blood found at the scene. We can speculate on how and why the kidnappers were successful at getting the women out of the house but we can speculate with high likelihood of correctness that it wasn't voluntary (Sherrill leaving cigarettes, Stacy barefoot).
I've never bought the idea that the Springfield women were targeted for something they knew or some kind of revenge. It may be that some event brought Sherrill and Suzie or Suzie and Stacy to someone's attention or to the attention to a pair or trio of killers. But the motive is almost certainly rape and murder for the sake of it. If someone was watching any of the three, the arrival of the girls posed an opportunity to fulfill some hidden fantasy.