I see you aren't getting a lot of answers here, so I'll jump in although I know nothing about your zone..
OK I'm in zone 4/5 ..Michigan..I find that the best things for me to chop and drop are things with large leaves..
I use a lot of comfrey, and also use the leaves when I harvest rhubarb.
I chop down the large leaves of my horseradish plants as well to use as mulch and I go out in the byways on my property and gather things like milkweed as they have large leaves as well.
I have read that you can also cut small leafy branches off things like willow and alder etc..to use as mulch..i haven't done that yet..but would be careful not to BURY anything that might
root in the garden esp the willow branches..just lay them on top.
I have no
hay or straw available easily around here as there is a huge hay shortage from Michigan's drought, so I have to make do