There is another thread here that has the offer codes so you can check availability online.

Basically, the code goes: HSxxN#
xx = the first two letters of the type of cert (eg Elite cert = EL)
# is the number of nights the cert is good for.

I imagine Hyatt did this because it deters people from booking this rate and then arrive without an actual stay cert. If you take the time to call (or have the resources to find out the code on your own) you're much more likely to also actually have the certs with you once you check in!

I booked each night separately because it gives you the most flexibility though it will probably mean that the checkin process will take a few minutes longer.