1.) Fill up inventory with items. Don't use bags, just put everything directly in your hotbar and inventory, until it is full. Equip armor as well.
2.) Set NEI to cheat mode.
3.) Save to an unoccupied inventory profile slot.
4.) Empty out inventory.
5.) Fill it again with other stuff.
6.) GOTO 3.)
You have (IIRC) seven inventory profile save slots. Meaning you can preserve seven full inventories in this way.
Then start a new world. Now you just load the first inventory profile, then store all the items in a chest. Load the second profile, store all the items... and so on.
Don't forget to turn cheat mode off afterwards!