Story ID: Immortal who ends(?) via Time Travel

Question

What I remember:

• The main character was some kind of heroic uber-man type (compared to, or possibly the inspiration for Doc Savage and others, if not actually him, using another name)
• The story involves a group traveling back in time to study ancient man (possibly neanderthals), tribal migrations, etc. Our hero seems to have better luck due to an almost animalistic nature he can draw on. (Think: jungle cat, in human form, occasionally showing it's teeth (metaphorically speaking), scaring the men and arousing the women.)
• Our hero ends up staying behind when they leave, with one of the women. (update Nope; she went back, but later met him via a subsequent time trip) I believe it's implied that he's now the ancestor of much of the crew if not much of humanity (and possibly himself.)
• After returning home, the rest of the cast finds the cave where he hid his diaries (and notes on history, since, by this point, he's lived thru most of recorded history), and it includes his speculation that when he reaches the point in time where he previously existed, he would probably vanish/die/something as the universe might not permit two of him to exist at the same time. (It's not stated, for sure, what happened to him, but they can't find him -- that said, he could well have discovered he was still alive, and chosen to disappear.)

At some point, I also found out that the character had a genesis in another story, tracked it down, and it involved taking some kind of difficult journey (thru jungles, and I want to say a mountain or dead volcano) to somewhere where he participated in a ritual (possibly involving drinking blood or some degree of cannibalism) that ended up rendering him immortal. I believe it involved the creation of some potion, and in the time-travel book (in the notes he left behind) he comments that he never learned the details of how to make it, so couldn't share it with the woman who stayed with him.

I THOUGHT (for some reason) it was Robert Hedrock (the immortal from the Weapon Shops of Isher), but it doesn't seem to be.

Answer 1

Time's Last Gift by Philip Jose' Farmer. Here's a link to a review

I thoroughly enjoyed this sci-fi adventure which put four scientists from 2079 into the past approximately 12,000 years ago to explore the rudiments of human civilization in the European continent and somewhat beyond.

This is the story of John Gribardsun, a dynamic and powerful man possessed of black hair, grey eyes and a peculiar animal magnetism who finds himself fully alive in this prehistoric setting. His company includes Rachel and Drummond Silverstein and Robert Von Billmann. These folks are on a four year expedition into the past and live among the natives they find, a diverse group of primitives who display a wide range of very human emotions and behaviors.

The story turns when it becomes increasingly obvious that Gribardsun has an agenda apart from his colleagues. The story is complicated when Rachel is attracted to Gribardsun much to the consternation of her husband. The story tracks the team and their adopted tribe across much of central and southern Europe and even onto North Africa.

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But then it becomes clear that Gribardsun's agenda means he will be staying behind and he lives among the tribe after the team does head back to their original time. That would be interesting enough, save that we learn Gribardsun is immortal and he then turns up again and again throughout history and even contacts the team again with an array of treasures, his many gifts from the mists of time.

As far as the animalistic nature of the protagonist, let's just say he's an analogue of Tarzan.