Visual
The next thing we did, was to draw a route from each place to the next, trying to minimize the length of the path. That went okay for the first 10 addresses, but after that there was always a next choice that made us wonder if we had the optimal route so far. To make a long story short: this didn't work out at all.
Algorithm
Also, we needed all the intermediate travel distances between all places for this. There as no way we could get over 6600 distances (82 x 81) in reasonable time without entering all seperate pairs apart in our navigation system.
Solution
Both the visual and algorythmic approach did not solve the problem. We got a tip to use this great online route optimizer RouteXL at www.routexl.com. That was the best thing that happened to us. We tried it for free up till 20 destinations and it worked great.
After we paid a small amount via paypal we could import all out addresses from Excel, calculate the fastest journey with the optimized order of waypoints in a snap, and download the multi stop route to load on our navigation device. I wished we'd knew about it before we spent several days working on our own solution.