Lets say for arguments sake, that a world, with maximum population of 5 billion, the common Joe gets reincarnated a few hundred times since the creation of humankind. This type of reincarnation is specific only to humans and didn't so much matter till record keeping was invented. The Old Soul doesn't have very many memories of their previous lives just things similar to what we have as deja vu. Looks, memories and more importantly the names, which are recorded at every birth determine what soul inhabits a baby. A child can grow, learn and have the childhood of any other without the thought that they have lived before. Only in strong instances can a memory surface. All they know is that there name is what ties them to where they grow up, their occupation, their role in the world of society.
The ether stores energy of converted souls (animals, dinos, insects, etc) to transfer the souls into bodies and every once in a long long time, create a new soul.
With that background knowledge, plausibly speaking, how would it be possible to keep the same group of souls continuously entering new bodies while others take longer? What could substitute the hiatus of a souls sleep to bypass decades and jump right into a new body after say, a week or so?