In a park in the burbs in my area, they had to do the same thing. They took out about 330 of them within 10 days - all at night. Then, they let 10 bow hunters in to continue the job. It was very controversial with PETA type groups protesting.
The funny part about it though, is that they announced when they would begin the cull, but actually had finished before their announced start date. They really pulled a fast one on the protesters. Just when the protests were reaching a peak it was announced that they were done. Too late to protest.
In these types of situations, the sharpshooters are really the only option. You just can't have regular hunters harvesting such a high number of deer in such a short period of time. It would have greatly affected the operation of the part also. As it was, they did it at night after hours when nobody knew it was happening. Also, they donated the meat to food shelters. So, much less wasteful than other culls and methods.