When is the best time to divide them and spread them out? Do I have to wait for them to die back? I am afraid I will forget which ones did not bloom, as other perennials come up and hide them.
Under the circumstances I would go ahead and divide them now, even though it is not the most ideal time. Something else you could consider though, is marking the clumps by surrounding the foliage at the ground level with surveyor's or flagging tape. You could even write some notes on the tape such as bloom description or anything that might help when you divide them.

Ideally one should wait until about 6 weeks after the bloom period has ended and then either dig and plant back immediately, or else dry and store the bulbs for planting in the fall once the soil temperatures have dropped to about 55 degrees or so.

I also need to move bulbs that are in places that are about to become brick and stone pathways. When can I start moving them?
I'd say under the circumstances, just start moving them now while they are still green.

Sue

Here is a link that might be useful: Flagging tape