I start with the three you mention, then I try Net-A-Porter, Barneys, Farfetch, Matchesfashion & Mytheresa.
Neiman's owns Bergdorf's so they normally have the same inventory, but I try them too.
I had great results (although somewhat frustrating) with Neiman's online. New styles are added almost daily. Check through the gowns everyday, the good sale dresses sell out and disappear quickly, but they may reappear again (returns?) If you find something, but it's sold out in your size, keep checking back. I found a $2675 Alexander McQueen gown that was perfect for me, on sale plus a 30% off code (I think it was $450ish.) I found the same gown at full price or on sale at around $1600 at 2 other places. Had the last one in my cart at least 4 times over a couple of weeks, then it was sold out right after submitting my order or my order cancelled. I was checking online nearly everday. It kept coming back online, though not always in my size. The last time my size showed up, the order went through and it's happily hanging in my closet. I haven't seen it reappear since. Also had the same experience with an Armani Collezioni short dress for another event recently. Both dresses would normally be out of my price range, so I'm thrilled. Neiman's frequently has 20-30% off codes if you're on the mailing list, so you do have to gauge whether it's worth taking a risk and losing out or wait for the extra off.
I haven't purchased from The Outnet, but they do have a good selection of gowns at pretty good prices.
I'm probably too late, however, this may be useful to others. Try Runway2Street. They've got up and coming designers, you'll find dresses that aren't part of the regular RTR line-up. I purchased several dresses as reasonable prices and received many compliments.