I am also a LA quilter but I have many uses for those strips of excess backing.
I don't cut down client quilts when they are completed so in those cases the client gets the excess back, still attached.
If a a backing is a tad too short for loading (have enough as a backing just lacking those few extra inches for attaching to the leaders), I use those cutoffs to add the needed length so I can attach to my leaders.
I've used them supplemented with another fabric to make a hanging sleeve.
Cut them into my binding (but like you I do prefer a bias binding if I have the extra fabric to make it or if I have curved edges)
Cut up into test squares and use them as my test areas off to the side when I am testing my tension. I test with every single bobbin change as well as color changes even if I never changed the thread type (IOW same brand and weight just a different color).
I do like scrap quilts so I also put them in my scrap pile and do use them a lot. I used a leftover batik backing as one of my lights in this quilt:
Scrappy batik HST quilt . I save any strip I can get at least 1 1/2" wide out of.
Tear them into strips and use them tie up tomato plants in the summer.