Mish - I've done a lot of moving in the past couple of years. Consider yourself lucky that you don't have to move out of one & into one on the same day when the folks moving into yours are in the driveway & your agreement was to switch the dishwashers from one house to the other & you've got a king size waterbed and it's an ice storm and New Years Day when no one can help. (Yes this happened). I didn't add that the furnace broke, the deal didn't close & I had a handicapped 5 year old, a 2 year old & a dog and a cat.
Just breathe! I would definitely hire a mover even if just for an hour to do the china cabinet. Don't risk something to save $. They could move the bigger pieces & the china cabinet & it would be worth every penny.
This time next week you will be in. Keep pushing yourself - the finish line is almost there. You can take your time unpacking & savoring this new chapter in your lives.
