If you can lift the whole clump keeping the soil round the roots and heel them in somewhere until the foliage dies down good and fine otherwise you need to let them die back before lifting - though other plants will grow up through the daffs.

The tried and tested way, take the heads off, lift shake off soil, place in tray with dry compost and store for replanting later in the year.

Next year why not save yourself a lot of time and trouble by planting your daffs in pots and then plant the pots in the "small" garden
This way you can just lift the pot out and put it behind the shed or any place out of your way and you can "right away" plant in the same spot the plant pots came from.

At the end of the summer just return the pots to the garden ready for next years display.