I own Garmin units (Zumo 660 for my TV and motorcycle, Edge 800 for my bikes ... as in bicycles) and in various scenarios, encountered the same challenge as you describe wanting to take a route slightly different from what the GPS wants.
If a significant diversion from where a GPS would want to route me, I will use mapping software to create a route and upload to my device (assuming your Rand McNally can do the same?). If simply an alternate route as you might see in Google Maps, I will make a few notes about the exit or road to turn on and allow the GPS to catch up with me and re-route or re-calculate.
As to the GPS jabbering about various interchanges, I keep the volume turned pretty low and rely on the visual ques on the GPS screen. Once in town where I need to be 100% focused on the road, I will have my co-pilot (who usually has her paper maps out as backup!) turn up the volume so I can hear the turn by turn navigation.
Hope it helps!