Good point, so I started thinking over how that might work without being just "they didn't think this through" - 'they' being either the writers or the characters, though at least the characters have the excuse that they were kind of desperate and jumping in without a real plan was the only option they had.
So perhaps - and I'd have to review exactly what G'raha said about it in the game to be sure, but - maybe they weren't aiming for him to arrive a particular point in time relative to the deadline, but rather at the earliest possible time they could arrive.
Note that I am running on the assumption that G'raha's arrival in the First does not split the timeline, because he has no prior knowledge of events there. There is simply never a timeline in which he does not travel there. (Compare our time-travel trip during Alexander - there is never a timeline where we didn't warp back and appear before Mide three years earlier, because that is part of the chain of events that leads to us being there in the first place.)
I assume that the timeline will only split at the point where G'raha's original future can no longer come to pass, and anything that happens prior to this point, even if it involved time travel, is simply incorporated into a single flow of time. Otherwise we broke the timeline already, possibly twice, and Alexander seems to think everything is fine.
SO. If I was a Future Ironworks engineer trying to calculate "when" we need to send the tower...
1. At what point should we try to contact the WoL? We don't want to somehow jeopardise our ability to invent the time machine in the first place, so to be safe we should wait until after they've finished dealing with Omega and Cid has that information. (I need to check but I believe Alphascape was released in 4.4, the same patch in which G'raha started trying to summon us.)
2. Having decided on that time, we need to decide the earliest time to travel to. We can't interfere with anything that the WoL knows to be true at the point when we contact them, or we might disrupt the timeline prior to the point where we're trying to split it. That means no stopping the flood or arriving on the First before Minfilia travels there to save it.
3. So we need to arrive after Minfilia departs for the First, and would like to get as close to that as possible so G'raha has as much time as he can to work out what he needs to do.
Of course, "soon after Minfilia departed" in Source time translates to a few years since she arrived in the First.
We don't know how summoning mechanisms work. Maybe there's some weird thing with bodies and souls, and it can't work with a soulless body. I think it's safe to assume that there's something preventing it, or they would have done it by now.
I don't think Thancred can use normal teleportation devices at all though, so maybe he wouldn't be able to use that one either.
And I really don't know whether to count the "summoning warriors from beyond the rift" as something that actually happened in the story or not. It's a really cool moment at the time, but it's just weird on so many other levels. Doesn't add up with the difficulty of summoning the rest of the time, and what happened from their perspective? Pulled out of nowhere, fight this monster they've been thrown up against, then snap back to their own world without an explanation?
As I was saying earlier, there's no proof that there was a "before" to be changed by the tower's arrival. It could simply always have been the case that it happened.
That's one of the weird things with time travel stories. It's partly perspective-based - if you go back in time to deliberately change something, you've got to contend with the paradox of "but how did you stop it if it never happened" (not that this has stopped the overall premise of the game's plot) and even if you do succeed, there must have been a timeline where it happened for you to be aware of it.
But if you simply time-travel with no idea what's going to be there when you arrive, there's no previous knowledge for you to clash with. You simply become part of that timeline as it is. We accidentally appeared before Mide and accidentally dropped the journal that would be mistaken for a book of prophecy. (Well, it was deliberate on the part of the cat who knew what it was doing.) With no expectations, we simply became part of that point in time, with the ability to influence our own past.
And of course the other time-travel instance in Alexander, where we save our earlier self... well, it's going to be a lot less straining on reality if you act to ensure something happens the way you remember it happening, rather than trying to prevent it.
Definitely not happening. We specifically broke the time machine's core in the Twinning.
I disagree on the possibility of multiple loops. There's been no suggestion of it, and it would spawn new "bad" timelines every time he failed.
Everything points to him regarding this as a single chance to succeed. If there was ever going to be a second loop, he's not on it yet.
You seem to have dropped the "begin quote" code from the start of your post.