Where I lived a number of years ago, I discovered through word-of-mouth, a high-end furniture store that saved all their incoming shipping supplies, set up one of their backrooms to recycle these supplies, and offered private outgoing shipping of large items via FedEx. They were able to recycle all these expensive supplies and bring in an additional income source for their business. I used them a number of times. They did everything. Their were EXCELLENT at packing odd shaped and large items due to the business they were in! If there was a question regarding an odd measurement, they would call FedEx direct to be sure they packaged in proper proportions for the least expensive rate for me. (I even had them ship a piano!) The cost to was low due to their using recycled supplies. I received very happy feedback from customers.
This may be something you could ask around about and call around about.
There are also many small stores, private furniture or appliance stores that will give you free recycled packing supplies (styrofoam peanuts, foam sheeting you could use for corners/legs/etc, large cardboard sheets or boxes, etc.). You'd be surprised what's available 'privately' once you start asking around your local area.
Good luck!