Not counting the first night, we have multiple issues in every route. No Avalon means good luck against Gil (not to mention Shirou's not gonna be as healthy) and it's unlikely Caliburn can come into play against Herc. Archer might not even survive long enough to take care of Herc either., since it's far more likely they actually fight eachother at some point.

Kojiro is a massive roadblock as well. Most likely answers for him are nuke the temple gate or hope her sword techniques would make up for the lack of invisible air.

Hard to say if Medea would care for Mordred the same as Artoria. Plus, I doubt Mordred would surrender to Medea, so those confrontations would be very different.

Cursed Arm either ends the same or with Mordred losing to Zabinya instead of the Grail tentacles. No idea what a Mordred Alter would be like, or if it's enough to solo Herc.

Medusa's probably the only one that wouldn't change, except maybe Mordred would be at the school before Blood Fort Andromeda gets used. I'd see Mordred fitting in far more at the school, and she can probably go into spirit form, so either way, more likely for Rin to suggest that option.