Pink: Moving is always tricky; I think the main reason for keeping 2 years, and working with all the spagnum etc is for seriously established trees (Say 10+ years in the say spot) and particularly for slow-growing species. The older the tree and the slower growing, the more time you would take.
So if you are thinking moving BIG trees, you should consider the two-step long term approach. If you are thinking the somewhat smaller younger trees of faster growing species you should be alright after a year. I have never filled a hole with spagnum etc.
The biggest tree we moved was a 4m tall, 6" diameter trunk Platanus. We dug a 40vm deep channel around the truns at 50cm distance, put the soil back in and left it for winter. In September (Later summer) we moved the plant. The first year the tree grew only 10cm. The second (Last) year branches grew over 80cm, so I think that workedout well. Mind you: Where I live is moist, cool and good growing conditions for deciduous trees.