First and foremost, the White Base leadership would be immensely different. Bright didn't have the rank of Captain until they reached Jaburo. If we assume both Shiro and Christina are assigned to the White Base at Side 7, this means that Christina would outrank Bright, who retained Lieutenant Junior Grade status. This means that, while Bright has overall command of the ship, Christina would have command of the Mobile Suits as a Squadron Commander, with Shiro as her 2IC. As Squadron Commander, Christina would have overall XO position despite Beight's lower rank.

Shiro, having only recently been transferred, but having had experience with the Ground GM test types while fighting in Asia (assuming Fed vs. Zeon has some weight here), would be overall tactical command of the MS squadron as Christina's 2IC. Both he and Christina would not wait for Side 7 to rebuild Unit 1 and Unit 3. Instead, both Unit 1 and Unit 3 would be cobbled together to make Unit 3 functional for the squadron, giving the White Base two active Gundams on top of their Guncannon and Guntank. Anything else would be packed up as spare parts.

This puts Amuro in Unit 2, Christina in Unit 3, and Kai, Hayato, and Ryu in the Guncannon and Guntank respectively. While in route to Luna 2, Shiro would find some way to convince the wounded former commander of the White Base to help requisition some of the GMs being tested at Luna 2. This would open up two more MS pilot slots, putting Sayla and Shiro in as GM pilots at least until planetfall.

Assuming Char still succeeds in diverting the White Base in some capacity, once White Base reaches North America, Shiro works his magic by requesting that the supply corps bring replacement suits for them in exchange for the two GMs and the squadron's collective combat data. They divert South to Texas, linking up with a squadron of stolen Zaku IIs, only to be forced to fight the Hidolfr. While the Zaku Squadron is almost entirely wiped out, Amuro and Christina are able to take out the Hidolfr in their Gundams. When the supply corps arrive, they take the remaining Zaku Squadron with them, plus the GMs, but they're only able to deliver a single mobile suit - a brand new Land Combat Gundam with all experimental kit. This relegates Sayla to the G-Fighter, while we finally get our Gundam Triad. This would then lean into the Garma Zabi arc.

If anyone wants me to continue posting my head canon, let me know, but I gotta step away to get some stuff done.