It takes about 6 seconds to build the rope. Maybe you could change the order of things like this: First go to bed and spawn Skeletron, then build the rope. Everything remains the same except that Skeletron is spawned earlier and now the fight has 6 seconds more night-time, so there is increased chance that Skeletron gets damaged by a falling star, or by something else.

The only down-side is that you need to survive Skeletron's attacks while building the rope in about 6 seconds. Is this feasible?

Building the rope while getting constantly knocked back by skeletron sounds very risky and would probably just lose time. If you are going to high-roll for early fallen stars it makes more sense just to not build the rope entirely. I've never run Skeletron at a high level though so take this with a grain of salt.

I don't think it can work, the fact that the rope is built first is because it is an essential element of the run and it only costs a couple of seconds that no matter what strategies you use you will still have to spend it. As for the night time, the probability of a star falling on the map is 0.125% for each tick of the game (basically it is very unlikely to fall), taking this into account we must add that the skeleton is aligned on the same Y axis as the character and the star falls diagonally so the chances of hitting the skeleton are even lower. I have speedrun the last seed used in the world record and in more than 100 runs only one star fell and it didn't even pass close to the skeleton. I have even tried to set up lineups so that if a star fell it would hit the skeleton but even with that it was not possible. Playing according to the stars seems very silly to me considering the amount of seconds that can be improved if you improve in other aspects such as: movement, route, menuing, etc.