UTM and MGRS and making custom maps.

I have recently started making my own maps of smaller areas I tend to walk/explore since purchased maps tend to cover vast areas of miles and I only need about 500 meters but in much greater detail. I also make up small scavenger hunts, like Geocash but more intricate and like a navigation race, so I prefer to use MGRS for the printed map since it is more intuitive for those who are not used to Deg, Min, Sec or decimal degrees. I am using QGIS which doesn't have a MGRS grid line option but does have UTM. I know that MGRS is derived from UTM so here is my question:
Using Coordinate Reference System WGS84/UTM zone 16N (I live in Illinois so I know that 16N is correct band) to create the grid lines and then simply remove the UTM labels and replace them with the shortened MGRS labels, what datum would I set a GPS if I wanted it to display MGRS coordinates and not be 10 meters off?

In case I'm not being clear on the details:

Paper map grid lines drawn using CRS WGS84/UTM zone 16N
Paper map grid lines labeled using MGRS labels for X,Y
I want my GPS unit to show coordinates in MGRS (not UTM since that has extra numbers), what datum do I set it to?

 

the "extra numbers" to which I refer are redundant when comparing to MGRS.
MGRS 16TDM3618129943
UTM 16T 436181.00 m E 4629943.00 m N

In the UTM Easting the first digit "4" and in the Northing the first two digits "46" refer to the same area designated "DM" in the MGRS coordinate, thus they are confusing if you tell a novice to "simply use the numbers after the letters but not the first number in the first group or the first two in the second group." MGRS is the ideal system to use for my application since all I have to say is "only use the numbers after the letters." provided that the map and the GPS are set correctly.
So,
Paper map grid lines drawn using CRS WGS84/UTM zone 16N
Paper map grid lines labeled using MGRS labels for X,Y
I want my GPS unit to show coordinates in MGRS (not UTM since that has extra numbers), what datum do I set it to?