Moving croci

I'm not entirely sure.  If you were putting them in the border I'd have said move them now, as moving bulbs 'in the green' is generally more successful.

However, as they are going in to lawn, is there a risk that they will get mowed?  If you cut off the leaves before they have died down, then the goodness won't have gone back into the bulbs and the bulbs will be weakened.

I always understood that the goodness in the leaves has to die back and feed the bulb... so I would wait until the leaves have gone brown (and crispy) and they easily come away from the bulb when very gently pulled... then the bulbs can be transplanted or dried and planted at a later date.

By the way...  I believe when the flowers die, that is the time to feed.