Aaron F, there is no *perfect* solution.
I used to be a pro photographer (NFL, MLB) as well as a photojournalist for a few papers. There is no perfect bag for what you want.
Some more thoughts on the matter:
1) A backpack with a strap pocket for your point and shoot. This will place the camera on your chest in front of your shoulder for easy access. If you get any decent hiking day-pack it will have attachment points on the straps. Any camera shop will have small bags that will attach there.
2) A photo belt pack system (fancy name for a fanny pack). I used the Think Tank Photo system with about 5 bags and lens holders. I looked like batman running down a NFL sideline but all the gear was easy to reach. 2 bodies, 15mm, 17-35, 80-200mm, 300mm (all f/2.8). Honestly, that's overkill for travel photography.
3) If you have just one lens on your DSLR, just use a fanny pack.
4) The very last thing I would use is a messenger bag (see my post about cavernous interiors). You don't want your gear rattling around bumping into other gear in one huge *unpadded* bag.
5) Gonna leave the gear in individual cases while in the messenger bag? Well, then now you've got a bag in a bag. You just threw "convenient" out the window.
By the way, I was a BMX freestyle photographer before I did pro sports. I had to haul cameras, lenses, lights, flash triggers, light stands, etc...on the BMX bike while humpin' it to the spots where the guys would do the tricks. I agree that a backpack is a pain for quick shots. But, a messenger bag isn't the answer.