My DD goes to a super tiny private school so I understand your concerns. DD could stay there next year too but it does not offer financial aid, which is totally understandable and I don't feel entitled to financial aid but bigger private schools around here offer need-blind admission. In our case, the school is not targeted towards gifted but it is somewhat self-selecting and it tends to attract families who want a non-traditional learning environment for one reason or another.
We are fortunate that within the tiny setting, there is quite a bit of diversity. Still, it is not the same as having a class of 80+ kids and being able to find your friends from a large group of peers. You go with what you have and I am not sure if that is necessary a good thing or bad thing but it does affect the social dynamics.
I am generally happy with DD's school but next year, I think we'll have to switch to partial homeschooling if she is returning there. We do have alternatives including charter, private prep schools, public, and online charter but I am not really feeling great about any of those options. In your shoes, I'd give the new GT school a try. If it doesn't work out, you can always return to the public school system.
