I am sure it would cost money to move these deer around, but not as much as you would think. I would take my truck and horse trailer up to bountiful and take a load of deer to a struggling area (especially if it was where I like to hunt). I am sure dedicated hunter hours could be given to do this. All you would really need would be to have a dwr guy or 2 at the trap site, and maybe one at the release site.
They transplanted deer out of an area when I was younger, and put radio collars on these deer. Yes, a couple left the area, but we saw many of these deer for years. I am sure some would die, but some would live also. If nothing else, maybe the predators would eat them and save a few that were already living there.