Truthfully it could have been any ship. I just made it the Logos in my mind since I figured if it could bring Neo back it was at least still flying. It could be whatever they built from parts they could find of all the ships. Maybe a new ship where the 3 captains share responsibility.
It's not actually very critical.

I agree it doesn't make a whole lot of sense for them to be flying around with Neo, but I think it's going to be 'fill in your own answer' type thing. I can't come up with a better plan that I can actually pull off.

As far as the opening, it's the same Seraph scene just with the V.O. removed. The V.O. is now used a little bit later in the film (very similar to the alternate opening I posted).

I will allow for a trim to Zion. Editing and zipping through it, it's not long, but it shouldn't be 1-1/2 minutes.

So the complaint was that the transition from the ship to Neo/Trinity holding hands? I can tweak that a bit.