While I originally planned to write out some Starclimber snippets as they would've happened in my headcanon, I decided against it because I don't want to rewrite scenes that already happened with only minor change. Instead, I will post my own timeline of when I think everything happened (I like to have exact dates for consistency), and describe briefly how I think Starclimber would've gone down.

Events in Skybreaker

Oct 21, 1912 (Mon)

Matt comes back from the Flotsam.

Oct 22, 1912 (Tue)

Jewels Verne, Pruss, Rath, meeting Nadira.

Oct 23, 1912 (Wed)

Heliodrome talk, departure on the Saga.

Oct 28-30, 1912 (Mon-Wed)

Finding the Hyperion and subsequent events.

Start of this fanfic

Oct 31, 1912 (Thu) — FFF Ch. 1-3

Morning after the escape, drunken night.

Nov 1, 1912 (Fri) — FFF Ch. 4-9

Night of dancing and revelation.

Nov 2, 1912 (Sat) — FFF Ch. 10-11

Next morning, arrival in Paris at night.

Nov 14 ~ 15, 1912 (Thu-Fri) — FFF Ch. 12-17

Matt fails his exams, Nadira comes visit, Kate gives the Yeti talk, the couple reconcile.

Nov 29, 1912 (Fri) — FFF Ch. 18

The couple's first date after their reconciliation.

Dec 21-22, 1912 (Sat-Sun) — FFF Ch. 19-21

The couple's first night together.

Dec 24-25, 1912 (Tue-Wed) — FFF Ch. 22

The Christmas party.

Jan 1, 1913 (Wed) — FFF Ch. 23

Nadira finds out.

May 27, 1913 (Tue)

Matt's 17th birthday.

Jun 7, 1913 (Sat) — FFF Ch. 24-25

Matt finishes First Year after 4-day final exam. Kate attends Conference in Lyon, and the couple spend the night there as a belated birthday gift.

Jun 9-20, 1913 (Two weeks)

Matt works on the Celestial Tower

Events in Starclimber

Jun 20, 1913 (Fri)

Babelite plot. Kate's 17th birthday. Matt gifts her a star.

Jun 21, 1913 (Sat)

Kate's aerozoan talk.

Jul 1, 1913 (Tue)

Matt returns to Lionsgate City.

Jul 6, 1913 (Sun)

Garden party at the de Vries mansion.

Jul 7-21, 1913 (Two weeks)

Astralnaut training.

Jul 12, 1913 (Sat)

Meeting Evelyn Karr.

Jul 20, 1913 (Sun)

Cycling in Stanley Park, thrown in jail.

Jul 21-22, 1913 (Mon-Tue)

Final trials and announcement the following night. Matt finds out Kate is engaged.

Jul 23-25, 1913 (Wed-Fri) — Start of the Elena arc

Matt takes Bronfman's place. Traveling on the Bluenose.

*Elena is born on Jul 23 in New Amsterdam, the day after the announcement*

Jul 26 - Aug 2, 1913 (One week)

Training before launch.

Aug 3-24, 1913 (Three weeks)

Starclimber expedition.

*Elena turns 1 month old.*

Aug 29, 1913 (Fri)

End of Starclimber. Matt proposes.

My take on how Starclimber would've happened:

Having already broken up once, the couple would be a lot more resilient this time around, and cherish what they'd worked so hard to repair. They would be a lot more comfortable around each other and a great deal more trusting. At this point they would also have been physically intimate for over half a year (Dec 1912 - Jul 1913). Given the presence of Marjorie, sex wouldn't be a routine thing, but it would still be a significant strengthening factor for their relationship.

In short, I don't see Kate's engagement driving such a deep wedge in between them as it had in canon. Matt would still be hurt, but he would be confident enough in himself to know it was the necessary choice for her. Kate would be more open and eager to show she wasn't serious about going through with the engagement (e.g. leaving notes, or even giving him a heads-up instead of letting him find out). I don't think she would have written the letter to Sanderson either.

In addition, their numerous exchanges during training and aboard the spacecraft might have played out with more humor and sexual tension instead of jealousy and doubt.

Finally, I think Kate would be more open to the idea of marriage than in canon. She might still reject the institution of it, but she knows Matt would never limit her. It would be interesting and not impossible to have her propose to him for a change, but that's too much work to rewrite so I'll leave that idea be.

Now, onward to the next arc. Please be warned: this will be difficult to write. I've written out many scenes, but there are way more gaps that need filling in this arc compared to the last one. I will try to keep my updates regular, but please bear with me.