Certainly not abnormal that Business availabity doesn't exist for 6-7 weeks out. However it is true that SQ availability opens up closer to departure. I has a First award, but booked in Business on 1 segment. 4 days prior to departure a First seat became available. AE changed it with no charge.
As far as award availabity on SQ's new B773ER - I beleive they are not releasing award seats on these flights given it's an "upgraded" product. The SQ forum may help you there.