I read this short story after 2017. It may not have been new but did not seem very many years old. It was in a magazine. I read the magazine online.
The protagonist has a trading post that I think exists outside all the alternative timelines.He seems to be trying to re-evolve humanity during the stone age. It was not clear to me why this task was necessary. He was giving stone age people lots of advice. He taught them hunting techniques. He played them classical music from relatively modern times on a wooden flute. He chose a -wooden- flute so it would rot away and not be found in the fossil record.
He is encouraging interbreeding between homo sapiens, Neanderthals and other relatives closely enough related to have fertile offspring.
In the trading post are Neanderthals and other species of humanity from other dimensions. Two are interested in trading for human ova from his dimension as they are suffering from the results of inbreeding.
The people from one timeline offer to trade a cure for malaria. The people from the other offer forty dogs, breeding stock, much easier to tame than the wolf-like animals in our dimension. The protagonist has only enough ova to make one trade and still leave the egg donors fertile. He decides to trade for the dogs who can hunt with humans and protect them and pull sleds.
The people from the dimension he choose not to trade with are desparate to save their own timeline and attack the people in ours.