Might be easier to put a space elevator up and set up an “ice cycler” that has a shitload of radiators and goes out in a highly elliptical orbit, that’s maybe carefully shadowed by earth. The ice is then transferred to the top of the elevator and exchanged for more water.

By ice cycler, I mean a vehicle sort of like a mars cycler, that, uh, doesn’t go to mars….

Or even better, use something like a space fountain. Using actual water as the kinetic mass. (lol.)