take my hand anyway

Some Context

Something I should establish up front the Eighth Doctor's chronologically latest pre-War companion was Josie Day from the titan comics (as she's the only companion Eight has while wearing his third, War-era outfit but from before the War) (okay the upcoming Big Finish thing is also set during that era but shhhhhhh its not out yet). Since Josie has no departure story and given the state of Titan is unlikley to get one, I assume that Josie was his companion when the Time War started, and was the companion who was erased from history during The Starship of Theseus. You know, Sheena/Emma/Louise. Her. She's Josie Day.

The Original Option

So the normal option basically is that the Doctor was travelling with Josie when the Time War hit, and The Starship of Theseus is right when the War starts for him. Then, later on in his timeline after travelling with Bliss and Cas and Alex he goes back to Dronid right as the War starts and tries to avert it, although he is ultimately unsuccessful. He then fakes his death creating the relic and runs around in the Time War for a bit before Night of the Doctor happens.

Pretty simple and straightforward. However, it has two problems.

Alien Bodies basically states that a) The Doctor regenerated at least once between his eighth life and the War in Heaven and b) while he didn't necessarily die on Dronid he did die - the Relic is very much not a fake. Neither of those facts is being taken into account in this option, which is what I thought prior to reading Alien Bodies. So. After sitting on this for a bit, here's what I really think.

The Better Option

Okay. So we know from Gallifrey: Time War that the Time Lords were resurrecting their own en masse, but the exact way this was being done isn't made entirely explicit. We know how Rassilon was resurrected, but his appears to be a special case. We also know the War was fought in many ways primarily through timeline alterations instead of direct battles - this is discussed at length in The Book of the War, and we see specific interventions in stories like The Last Days of Freme.

So. The Time Lords have the power and the capability to resurrect the Doctor. Let's roll with that idea for a bit.

So the Eighth Doctor was travelling with Josie Day, and then something causes him to regenerate. No idea what and for this conversation it doesn't really matter. Let's call the result the Infinity Doctor. This does tip my hand where I'm going with this, but I already did that in the title so whatever. In any case, it's unclear if Josie left before or after the regeneration - I'm gonna assume after, but I have zero evidence of that.

That being said we actually do have some idea of what the Infinity Doctor did after parting ways with Josie - he went back to Gallifrey.

If you haven't read The Infinity Doctors, it's incredibly ambiguous as to when it takes place. It features an ambiguous incarnation of the Doctor living on Gallifrey, teaching at the Acadamy and serving on the Supreme Council. One of the best clues to placing The Infinity Doctors is that it also features a character called The Magistrate, who is implied to be the Master and the War King, which, based on the Magistrate's position and characterization, would place this during the timeframe when the Master was working under President Umbaste. Since Big Finish's account of Gallifrey jumped straight from Enemy Lines to the Time War, this gives us pretty free reign to do what we want during that time, and I certainly have taken advantage of this.

The Book of the War and Crimes Against History state that in the leadup to the War, there was a Head of the Presidency who followed (directly or otherwise) Romana. When the Master brought news of the existence of the Enemy to Gallifrey, the Head of the Presidency attempted to travel to the supposed Enemy homeworld and create a colony there, mostly just to prove the Enemy didn't exist. Said president's severed head was returned to the Gallifreyan High Council with a note saying "We are not amused." A Time Lord named Umbaste was installed as President, with the Master becoming Umbaste's proverbial right hand. Umbaste kills himself a few years before the War kicks off, and the Master becomes War King, ruler of Gallifrey in time for the War.

If you've not seen me say elsewhere, I think Livia Caralis was the Head of the Presidency, and after she was decapitated, she was reconstituted in secret by Project Revenant during Umbaste's presidency. After Umbaste killed himself, Livia returned to the Presidency, with the Master becoming the War King of the War Council, instead of taking the Presidency (note how in Time War how Romana is head of the CIA, neither Trave nor anyone else is said to head the War Council). Livia has the Master/War King act as the public leader of Gallifrey from the perspective of "lesser species" - of which The Book of the War (which, as an in-universe document, is not guaranteed to be accurate) is targeted at. Livia claims she was assassinated and needed time to recover, since her mission to the Enemy homeworld was only known to the High council. So with that all stated, the Infinity Doctors would take place during Umbaste's presidency, while Livia was still being reconstituted.

(oh and the nature of the War King was hidden from those outside the War Council which is why Romana and Narvin don't know that the Council is being run by the Master during Gallifrey: Time War 1-2. They probably knew that the Master was on Gallifrey during his time as the Magistrate, but from their perspective he would have just disappeared around when Livia returned.)

So, in summary. The Eighth Doctor regenerated, left Josie Day somewhere, and returned to Gallifrey and stayed there for some time acting as a teacher and a diplomat. All before the War.

The side stories in Alien Bodies gives us a pretty good idea of what the Doctor was doing in right before the War - specifically with his comforting of the dying shift-to-be and his confrontation with the Celestis. And then the Doctor is stated to die - although the circumstances of his death are unknown - and his body is taken to Dronid. All as seen in Alien Bodies. This all would be roughly contemporaneous with Celestial Intervention - I've said elsewhere that I believe the War was declared as a result of the destruction of Phaidon, and the first battle was then fought on Dronid. The Book of the War makes it clear both sides knew Dronid would be where shots were fired, so the Doctor was presumably on Dronid while Celestial Intervention was happening.

It presumably takes some time for this news to reach Gallifrey - in Time War 1, Romana assumes the Doctor is still alive. But Gallifrey (more specifically Ollistra) knows how helpful the Doctor could be, so a timeline intervention is approved to resurrect him. But because the Doctor (apparently) died in the colossal fucking temporal mess that Dronid had became, pulling him out and resurrecting him from that point was basically impossible.

So what Ollistra and her cronies do is timescoop him from previously in his timeline. She (or her people) pull the Doctor from out of his Eighth life and dump him in the Time War - and into the story The Starship of Theseus. Josie is almost immediately getting destroyed by the ensuing paradox (since she had a future that now can't happen since she got pulled into the War) and the Doctor is left scrambling to figure out what is going on. From his perspective, he went straight from travelling with Josie to in the middle of the Time War. And so he goes onwards from there and any wartime Eighth Doctor stories take place after that. Its possible the Doctor worked out later that his timeline was altered, but it is also possible he didn't.

For the record, I think Ollistra was behind the Doctor's resurrection simply because she seems the most invested in using the Doctor in the War, and because there's nothing we've seen from her that would prevent her from doing so. Like, the Master would have also been in a position to do that, but if the Master had resurrected the Doctor, there's no way they wouldn't have brought that up during any of the two's NuWho confrontations. I suppose it's possible that Mantus or Livia or someone along those lines could have authorized the resurrection instead, but Ollistra feels like the most logical choice.

I've spent this whole time breaking down the start of the War, even though the question asked about the whole War. However, given how the War In Heaven timeline has the Doctor die at Dronid (more or less), the Doctor doesn't really have any appearances afterwards in the War in Heaven works. So once the Eighth Doctor is up and running again in the War, from then on it just proceeds basically as stated by Big Finish and other producers of Doctor Who / Last Great Time War stories.