I just tried a very simple itinerary LHR-LAX-HKG-SYD-DOH-LHR, business class, departing in April
The first screen accepts the itinerary OK
But I cannot move to the second screen (to choose flights)
The error message against the LHR-LAX segment is:
"For the date you selected, we were unable to find any availability, please select an alternate day."
I've tried numerous dates in April with the same result
Expertflyer says there's plenty of availability on AA and BA non-stops

ETA Congrats on your first post OP