I used to drive that area about 3 times a week for several years back about 8 years or so ago
I honestly can't recall seeing a lot of deer, but I did see Pronghorn occasionally and there are plenty of yotes
I know there are deer out there, but that area especially where your family property is is ROUGH it is small sand hills with brush and not much else......it is one cow calf pair for 40+ acres type country
it sounds like your family property is or was part of the 2B Ranch
if you need a place to stay when you are out there you need to stay here
http://www.newsomvineyards.com/bb.htm and they have been in Plains for several generations now and can tell you all you need to know
eat at Lalitos in Plains as well other than that B&B you are staying in Brownfield or Denver City if you need a room
I know the deer pressure is pretty low because the family that owns that B&B linked above also owns the larger vineyards in the area and the deer pressure on the grapes is next to nothing and when I ask about it the answer was "they see them out there sometimes early in the morning" and that is about it
I would say more so baiting them in with food you wold be baiting them in with water it is PARCHED out there most of the year
there are tons of circles of peanuts and wheat/rye and sorghum along with the cotton of course and again I never recall really seeing much if any deer out there in the circles eating I was usually making the drive in the 10am to 11am hour though and back home 3pm to 5pm
I never recall seeing much of anything in the way of road kill either (you would have to be the worlds dumbest deer to get hit out there though), but there are not a lot of buzzards so if there was a road kill it would have been there for a while to see
Honestly I think I saw more turtles than deer
I would hunt it for sure, but I would be baiting with water and out there in the EARLY AM and I would talk to the people at the link above if in the area (they are not big hunters, but they know the lay of the land and when and where the animals move and they probably know your family or extended family especially if that is old 2B Ranch property)
now if you shoot Dove that might be a whole different thing....but that is a LONG way to go to shoot Dove and where your family land is you will still need to bring them in with something (and baiting is illegal of course), but you can probably plant Sorghum patches and shred it and be OK and of course any water they will be looking for
I am free and willing to go and scout it out for you 
