First off what kind of gifted program is it? Are they only focused on the high achieving kids? High achieving & gifted kids? Gifted kids regardless of achievement? What is their experience with 2e kids?

My DS's behavioral issues magically disappeared when he switched to a gifted class with gifted peers and with a teacher that appreciated and accommodated 2e kids. In our case most of the kids had issues in the mainstream before being selected for the program and the criteria was based on IQ scores (not achievement). Frustration with both e's were at the base of his behavioral issues so once the frustration was decreased for both he was much better behaved. If we had thrown him into a room of competitive high achievers and/or didn't properly accommodate his LD I suspect it would have been a complete disaster so I think the type of gifted program is key.

If it isn't limited to high achieving kids is there any chance of doing a trial of some sorts?