Here is my Promethium Ship, inspired by (ripping off) StupidFatHobbit's ship from his yt.
It takes ~40 minutes per trip, carries 128K eggs comfortably (I'm positive this can be pushed further with no other changes needed, but I don't need more science than this rn) and makes 384K science per trip. It travels at 464 km/s at all times.
I filled the ship with turrets and accumulators just in case of a biter mutiny, but this has never once happened to me, so many of them could likely be removed without consequence. There is also an automatic biter ejection system set to dump eggs 27 minutes after the first egg arrives (this can be adjusted in the first combinator below the hub on the left side).
Refinements could still be done, it seems that for a brief period at max distance into it's journey to the shattered planet it fires very slightly more rockets that it produces, but not enough to really worry me. In fact, the second layer of rocket and laser turrets seems unnecessary, but I haven't experimented with removing them.
I have also included the rest of the infrastructure needed, including biter launcher and "bathroom key system". This is a system that only allows one ship (if you have multiple of these) into Nauvis at once to avoid any conflicts with requesting eggs, by having a single rare barrel that is needed to progress in past Aquilo, and dropped back on the way out to the shattered planet.
I currently have Railgun shooting speed 11, Explosives 19 and Lasers 19 researched, but I strongly suspect they don't need to be quite this high for it to work.