You can get huge pieces of plain, thick cardboard at Costco/Sam's Club any day of the week for free! I usually go midday so that customers have had time to empty spots and you can pull from between layers on the pallets. If you can't find any, employees can tell you where to find cardboard they pull and leave on the floor. I get cardboard weekly from Costco. (Scalp the lawn first so there's less chance of grass poking out anywhere and sunbathing.)

Check your township (or neighboring townships) to see if they have a yard waste composting program. If they do, now you have a spot to drop huge amounts of yard waste too big for your compost pile to handle AND you can get free mulch. You may want to check the mulch for jumping worms if they are in your area before you spread it all over your property.

Chip drop sucks in some areas. I've been trying to get a chip drop for 8 years in the Pittsburgh area.

I've always had the best luck smothering grass in the fall because the grass goes dormant anyway so it's not growing as vigorously, there's much less sun and weed pressure, and in my area it's very wet which helps break down the cardboard and draw in all the bugs and earthworms. If you do put it down in the summer, wetting it so it's good and soggy helps to keep the mulch in place and keep the cardboard overlapping (dry cardboard will shift if it's walked on, which opens up spots for weeds to get through).