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If you are running software version 5.8+ then it is worth checking the settings in Setup > Routing... 
When a new Activity is selected this changes the list of entries in the "Avoidance Setup".
When Activity is set to "Automobile Driving" one of the entries you can disable is "Unpaved Lanes".

Unfortunately neither BaseCamp nor MapSource will display more than one mapset at a time.

An alternative to multiple uploads with the need to rename the gmapsupp.img file name is available with Mapsource...

If you open your first mapset with Mapsource and select all the map tiles you wish to download then switch to a different mapset and continue selecting map tiles when you finally download the maps the usual gmapsupp.img is created which includes all the mapsets selected.
The seperate mapsets available are still shown seperately on the GPSr unit and they can still be enabled/disabled independently as usual.
I think the only limit is a physical file size of 4Gb (fat32 limit?) and max number of map tiles on the whole device not to exceed 4000.

So you reloaded the map of Arizona...
This would create a file "gmapsupp.img" in the Garmin directory on the unit.
Now unless you rename this file, every time you download a new map it will over-write the "gmapsupp.img" file.

Just to clarify - Garmin does not give you a way to rename a map on the eTrex - you have to attach device to PC/Mac, browse to Garmin directory then rename file.

Once the "gmapsupp.img" file is renamed (Arizona.img) then the next map loaded will create a new "gmapsupp.img" map file which can be managed in the same way.