msv, regarding
BridgeClimb, the twilight one was the best one to do, IMO, but the pricing has been adjusted accordingly! Quite a premium now. Pricing is in the link - see the second set from July 07.
Perhaps you can e-mail the company to find out the actual time that the last 'day' climb gets out onto the bridge. Check the bom.gov.au website for the Sydney weather forecast, which also gives the time of sunset.
A slightly cloudy day is fine, for a more interesting sunset; August is probably going to be okay for weather, but if there is too much rain or cloud the week of your visit, maybe try to book the second day of your stay, with the option to defer/raincheck to the following day if necessary.
My wife (gf at the time) and later I have both done the walk and really enjoyed it, but would recommend you go at the earliest or latest walk of the 'day'. Night view is OK, but better to do that from the
Blu Horizon bar!