Given the independence in time of the multiple parallel lifetimes, does this explain then why a person can receive significant and thorough healing that extends as well to all of their influencers through all of time, without the risk of preventing them from being born into their current life?

This is very much the case. You can see more clearly with this model that the risks are much, much less than you would think because the parallel lives, while involving the individual, have a separate track and separate path and a separate destiny. This serves to keep them distinct and separate from the greatest of influences. For example, someone dying in a parallel life does not end the current life. So, one cannot use a more extreme example of independence than that. When lives begin and end, in periods of difficulty or torment, they will have an influence on the current life with respect to whether it is happening close or far in term of the juxtaposition of the time loopings. That is a complex issue. In a sense, all are on an even plane because all are happening in the current moment but yet are separate in a sense, separate but equal. So, the saving grace is they are not all being experienced by the part of the soul within the current timeline and the current life. They may resonate from a distance being in parallel life experiences but will not be a governing factor, for the most part, nor will they cause a permanent alteration that undoes the current lifetime or might prevent it from taking place altogether. This is the scenario always threatened in the science fiction movies about violating the space-time continuum where people might cease to exist if they change something in their past and the destiny changes accordingly. So, their parents never marry, for example, and so they could not give birth to the protagonist and in a sense, it ends up killing oneself to alter the past. This will not happen. It's not that it cannot be arranged, but that is different from taking active steps to better a situation. The divine realm can see in all directions and chose a strategy that minimizes any kind of complication causing that level of disruption. When extraterrestrials go back and forward in time, there is due regard given to the consequences as well. They may attempt to engineer the orchestration of human experience to worsen things, and this is honed to a high degree and is a source of pride and enormous satisfaction to them because it is the greatest demonstration of technical and scientific prowess that they can do such things. This is the way they can counteract mistakes and stay ahead of humanity with their designs on eliminating human influence, but it does not mean they will be successful. Humans are resourceful, and in appealing to divine realm, they are appealing to a level of consciousness that sees all and can bring about unique strategies to countermand such doings and to restore a more even playing field. This will continue to support humanity as long as humans choose to partner with the divine for their betterment.