Popping up by a group of rabbits only 12ft away is always going to be hard - that's only four yards! Did you mean 12ft or 12yds?
Long grass can be a pain, I'm finding similar problems of line of sight being blocked when lying down.
From the rabbit's point of view, what background is your head set against when it rises into view? Is it scenary that matches your headgear, or is it sky? If it's the former, rise up real slow; if it's the latter, then it ain't going to get better than you've already managed.
If your second method succeeded, then there's not much to say against it, especially if you got a wary buck. I guess you can worry when it fails to work a second time.