Being on the Mac BaseCamp forum, I assume you want to use BC. I would take the start and end points from Google and let BC create the route. If you don't get the route you want, change preferences in BC or drag the route to reshape. I am not sure if your GPS accepts uploaded routes, if not, just drag over the waypoints used to create the route to your GPS plugged into your usb port. Go to you favorites and calculate your route on the GPS.
I tried the link that converts Google map route (directions) to a gpx file. I did a route form Dahlonega, GA to Bowling Green, KY. I imported gpx file to BC and it had 19 waypoints to define the route. The route was direct routing between the 19 waypoints. I recalculated the fastest route and BC took the bypass around Nashville, TN but the Google Maps route went straight through on I 24. I recalculated using the shortest preferences and my route left the interstate in downtown Nashville, TN. Both shortest and fastest took me up I 75 a mile and over the exit and back down I 75 to get on I 24 west. The gpx file placed a waypoint a few feet past the I 24 exit on I 75. I wonder if the 19 waypoints and the ones you have to add or move to get the same route you had in google earth will give the same route on the GPS.
If I'm following your example properly, I think the problem is that Google maps and Navteq maps do not always line up the same way. You have to check each waypoint very carefully -- the one at the I-24 exit is a perfect example. Just a few pixels off and the whole route can change.
Yes, the waypoints is half the problem but BC is using a different algorithm to redraw the route and when you add preference setting to the mix, it worse than trying to get the same route drawn in BC and your GPS.