This would have made an excellent case study into YMMV. Having had some luck with them last year on a mixed-class redemption (mind you the Enrich team were based in Malaysia back then), I tried doing a similar gig this year.
9 calls later only had I managed to get it done, 3hrs altogether.
The entire team is now in Fiji, and seems that they work 4hr shifts over the clock. From current experience, shift change seems to occur 2pm (Fiji time), 6pm, 10pm and so forth with the 6pm - 10pm being quite "difficult" IMHO. Long story short, I would recommend trying the 10pm shift which is where I finally got my break.
The multi-class booking seems to throw some of them off - I currently have an X + Z class on CX simple layover - which some of them either insisted in ticketing as 2 separate itineraries (despite clearly seeing <24hrs gap), saying it was "not possible" to mix 2 classes in 1 ticket, being unable to calculate taxes due to mix-class search, married-segments, awaiting confirmation from Cathay desk etc.
Have fun