I've changed a mountain of award seats. The following is copy/paste from a classic award booking...
Here's another copy/paste
14.7 Classic Awards (excluding Classic Awards forming part of Combined Classic Award Bookings) - changes to tickets
14.7.1 Except as otherwise stated in this clause 14.7 and clause 14.8, changes are not permitted to any Classic Award at any time. Any permitted changes are subject to Classic Award availability.
14.7.2 If a booking is made that includes non-Classic Award flight(s) and Classic Award flight(s), then any changes to any Classic Award flight Segment or Segments in the combined booking may only be made in accordance with the conditions outlined in clause 14.8, and this clause 14.7 will not apply.
14.7.3 Prior to ticketing, Classic Awards may be changed without incurring a Change Fee; however, any changes will be subject to this clause 14.7 and to the advance purchase and validity provisions set out in clauses 14.2.2 and 14.6.1.
14.7.4 Subject to this clause 14.7, the following changes are permitted to a Classic Award after ticketing and prior to commencement of any travel and will incur a Change Fee (see the Fee Schedule) per passenger:
(a) change to flight number;
(b) change to date of travel;
(c) change to class of travel;
(d) change to any Segment routing or airline;
(e) change to name (only for Flights with a Qantas (QF) flight number on the ticket that are operated by Qantas); and
(f) request to cancel ticket and re-credit Points. Please note that only Points that would not have expired will be re-credited.
14.7.1 pretty much covers it.
I've certainly been able to change a U class award to an earlier flight with empty seats but I'm certain that it's not a "flexible" ticket and the T&C's do not suggest that it is either.