IMO, the most economical way would be to use a pull behind gang mowing in an up and back manner, but have a light weight fwy mower do the clean up pass and any other tight areas...up by greens, or around fwy bunkers. (I don't care how good of an operator you are it's really tough to keep a consistent edge with a pull behind gang)
Yes, you could tear up the approach, but you can tear up anything with bad operators. If the lightweight unit cut the approach perpendicular to the line of play, out 30 yards or so from the green, then the tractor unit wouldn't need to turn right in the approach. If the operator is careful and well trained he shouldn't tear anything up (especially if the course is kept dry).