For anyone wondering what use the addition of cycle-markings along the Canning St - EICC-car-park-entrace section of the WAR could be:
A: You can get directly from Morrison St to the WAR:
Enter the entrance slope into the magic automatic car park (deceased) between SWIP and the EICC/ATRIA extension.
Turn right into the magic automatic car park.
Turn immediately left to join the exit slope.
Turn left at the bottom and proceed west, watching out in every direction for delivery vehicles, until you reach the two-lane exit point to get onto the WAR.
Ride around in a small circle in the left-hand (westbound WAR, so motor-vehicle-only) exit lane until the traffic lights detect you, then escape to the eastbound WAR exit-filter.
Alternatively, you could go east to the Sheraton/Conference Square/Exchange Crescent car-park access section and either get onto the WAR/Canning St that way or run up some stairs to either Festival Square or Conference Square.
B: You can get indirectly from slightly further east along Morrison St to the WAR:
Go down Chuckie Pend between Macdonald Cycles and whatever the premises on the other side currently are, as if you're going to go behind the Filmhouse to Festival Square.
Beyond the end of the cobbled bit, where the path narrows between a shrubbery and the side of the building on the south side of Festival Square, look for a short desire-line path on the left leading to a small corral of skips and bins. Follow the footway down a slope past the bins, then repeat the steps above for not being flattened by a lorry and extracting yourself from the EICC delivery area.
It would also be possible to go from the WAR to Chuckie Pend by reversing this path after going along the new cycle lane westwards from the Canning St/WAR junction.
It doesn't look technically legally possible to go from the WAR to Morrison St by going up the magic automatic car park exit slope as you would be defying the arrows painted on the road.