In bloom would be better than right after bloom if you are racing bulldozers...but then in that case, any opportunity you have would be better than none since the plants will be lost if left in place :)

Moving them during their period of active growth is generally thought to be least successful timing (notice I didn't say no success at all). The period of active growth is while the new foliage buds are elongating and unfurling, immediately after bloom.

I answered you on the timing, when maybe you were asking about the procedure...

They will have a network of fine surface roots that extends out as least as far as the widest branches, and a few heavier anchoring roots. A shallow, wide rootball. You can take a smaller diameter rootball - aim for diameter equal to approx 2/3s the plants height if possible. Careful not to plant any deeper than they were originally growing, mulch over the rootzone to conserve moisture and cool the soil. They will need extra attention to adequate water this first full year.

In extremis, I've had to transplant azaleas and rhodies while in full bloom. I used a product called "Bio-Plex" or "BioPlex" which advertised that its use can make transplanting more successful even in the height of summer. I can't say for sure that the BioPlex made a difference, since I didn't move any plants which were not treated with it, but I can say that all of the plants survived the transplant (though not all survived my subsequent neglect and my woodland fauna).