My sister-in-law received her grandmother's china - packed by God knows whom. It came in pieces. She was devastated. I took the pieces to a crafter friend who makes garden stepping stones with china shards and she did a marvelous job on some images important to my SIL - she got some and so did her daughters, but it's not the same.
Split it up. For several reasons. If anything breaks, at least there are other boxes. Get a big old roll of bubble wrap from places like Staples or other office supply stores. Fed Ex stores sell the same thing - check prices. The rolls are perforated like paper towels but you can cut further to size if needed.
By all means, talk to the pro shippers, but this is not something they can replace if it gets broken. A TV set or vase is different from an heirloom. If I were doing it, I'd go down to my local liquor store's stash of free boxes, and get some of the dividers that separate and protect wine bottles. I'd separate/flatten those and put them in between plates and bubble wrap. So, plate, bubble wrap, cardboard divider, plate, bubble wrap, cardboard divider.... Cut the cardboard for bread plates and saucers. Take extra care with teacups or serving platters or sugar bowls that have handles - double wrap those. Plan on boxes with a whole bunch of air so you aren't packing things too tightly. And don't pack anything too close to the sides of the boxes. Get a roll of packing tape and secure the bubble wrap around each plate, saucer, etc. Don't just assume a sheet of it will protect enough - you want to be sure things are cushioned if they shift side to side, not just with weight from above.