In this setting people made many impossible things so lets make one more.
Lets made orbital tube transfer system around the sun. This system takes orbit between Earth and Mars and consist of rings. These rings forms space gas flow. The biggest speed of gas in the middle of ring and the lowest on the boundary.
Each space ship need a few fuel:
1. On the way from Earth to the Sun Ring.
2. Some fuel to smoothly reach the quickest space gas flow.
3. Smoothly goes out from Sun Ring.
4. Travel the rest of the way to Mars.
Lets see check list:
• It has to move very fast, capable of traveling from the Earth to Mars at their closest points in only 2 days or less. Also even though we did crack FTL travel, it is way too expensive to scale up past individual star ships.
Actually no. This system speed up all Earth-Mars distances excluding the shortest one. So this system doesn't solve the problem but it reduces the problem just to make Earth-Mars travel by shortest way in two days.
• It has to have a quick turn-around time, making it possible to unload its passengers and payloads, undergo a quick systems check, restock, reload, and depart in a matter of minutes.
Lets imagine letter container which can drop current letter on the fly and catch the new one. It seems possible.
• It has to be small, carrying only groups of 100 people each alongside a payload weight of only 5 metric tons each. For cargo only pods, it could go up to 10 metric tons.
Supported, this system can't work with big freighters.
• The UER is almost a type 1 civilization, so dyson sphere satellites and laser driven photonic propulsion are on the table (it’s not necessary, but recommended for cutting out fuel weight)
Fuel is not excluded but you don't need fuel on the ship to travel. 199
Just for manoeuvres.
• Although the bulk of the colonies’ populations are planetside, there are O’Neil cylinder space colonies and space elevators around each of these colony worlds. So, the surface to ground and orbital infrastructures are already in place.
It is possible to use it.
UPD 1. More details.
We have a set of tube transfer stations. They collects solar energy and speed up space gas flow in tunnel. There are container ships in gas flow which catches/drops usual space ships on transfer stations. I added Earth-Mars space ship trajectory to show how it works.
UPD 2. Shortest path. My previous picture doesn't use the shortest path. Lets make it shortest. Actually the ship orbit smoothness depends on speed changing possibilities. In theory we can improve the system if made satellite bus. The satellite bus is a big asteroid. This bus has elliptical orbit around the earth and can transfer smaller ships to transport ring. There is no such asteroid on picture now. 199