How is the fit of the cover to the core?
My climbing device milked enough newish htp to get baggy beneath the device, preventing it from working. I haven't washed or milked the rope. I kinda rely on rain to wash off the braiding wax (half hoping, half joking).
You have an excess of cover.
Some people use some of that milked cover to make a tapered end on the rope for tight forks, possibly also adding a loop of throw-line into the end of the cover for a clip-in point for installing, I think.
I might consider enough of a throwline loop to be able to girth hitch onto the ring of the throw-weight, as often will simply put the rope through the ring, and tie and overhand knot as a stopper. Not always streamlined enough. No stopper would remove some of that difficulty, while allowing the benefits, both speed of connection/ no loose equipment to misplace or lose and positioning of the rope.
Having a throw-weight at the connect allows for certain rope-installation finesse tricks. It manipulates way differently than a rope/ throwline combo, if you can afford the lack of it being as streamlined, to pull through forks.