First, even before considering demographics.
The main problem is, with ageless bodies, the pressure to have descendants lessen or may completely disappear. This kind of immortality brings a whole lot of problems and changes, which are partly solved by the limited numbers of souls. Overpopulation for one.
The elf civilization will have two repeating stages. Growing and peak.
The growing stage:
The elf population starts with low numbers. They will have limited and pretty unbalanced civilization, scaled towards the oldest and most knowledgable surviving elves talents and interests. They will make baby elves regularly and without care. The oldest are honored as keepers of knowledge. There may be elves out there who lived through numerous civilizational cycles. Their lifespan will be truly ageless and transcendent from worldly affairs, creating a mini council and sociaty of their own, to guide the "repeaters".
The peak stage:
The elf population reached its maximum. During the growing phase, there may have been conflicts during the families, but they put that behind themselves, by either uniting under a single family (ohh, sooo much incest!!!) or various families coming to agreement. The latter shouldn't be hard as with ageless bodies, much of the biological pressures which causes conflict are mitigated. You can simply wait your turn, improve existing technologies to have more.
The oldest elders are still honored, but there will be a shift. Having a child will be viewed as a gift, a blessing for those who want them. The youngest will be focused on by the whole community and they will be mini celebs, with all the resources at their disposal. Which will spoil them rotten, hastening the collapse of peak stage. Just look up the chinese little princes, with four grandparents. The same here just worst!
Babymaking will be either heavily regulated. It may reach sacred, ritualistic levels with priests and observers as the couple "summon" the spirit repeatedly. (Elf porn ftw!) The right of having one given to the priviliged or those who are next in line. Or they will slowly descend to nothing else but constantly trying to make babies, to increase the chance.
The truly desperate may kill the fellow elves to "free" their spirit... and fornicate on their victim's dying body to capture its spirit (Ghostbusters elf edition?) ... And its just part of the fun. In a max out population, with managable numbers like one million, each death is quickly noticed. A new pregnancy too. Which will lead to "spirit" lineages and other esotheric stuff.
The parents will give birth to the killed elf, good things memories aren't carried over... the dead's family will see the newborn as a lost loved one come back, made worse that relationships may lasts hundreds of years. All kind of insanity and craziness ensue, which will lead to the collapse and mass death of the elves.
The cycle will start anew, with the lead of the wise old who may have many such cycles behind them. Some of those may try to fix the problem, some may be dumb to the whole thing, as they lived through it so, so many times. Suicide among those may not be uncommon or negatively judged...
It would lead to all kind of interesting tradition, worldviews, religion, temperament, technologies and individuals, especially among the truly old.