Like most of us I have a few bags (and have owned many more since the days when I first started photographing in the mid 1970's).
For my "daily" bag, I use a Billingham Hadley (M6 TTL + 4 lenses + film + iPod + wallet, keys. Very comfy and easy to use. I had a Lowepro "Stealth Reporter" at one point (a large one) and it was a nightmare for the reasons the OP outlined.
I had (still have) one of the original Slingshot 300 bags but this also opened the wrong way round andstuff fell out as it was facing away from the photographer. I wrote to Lowepro about this to see if anything could be done to improve what was, otherwise, a great bag. At the next "Focus on Imaging" show, I went to the Lowpro stand and met up with the Product Manager. He explained that they'd just introduced a new range called the "Classified Sling" which, when slung round to the front, opens up with the enrance at the top and the hinge on the far side - away from the photographer. This makes it easier to get into and also feels like you can keep your kit away from prying eyes / fingers when travelling.
I have the 220AW version and my wife has the 180AW version. Great pieces of kit. Comfortable, practical and not "obvious" as being camera bags. Worth checking out.