Hi,
Welcome!
From hanging around here for a while it seems like all kids are different, some very gifted kids seem to get a lot out of a regular setting and not mind the boring parts. I know one gifted looking 3 year old (not mine) who loves the social aspect and is just easy going so doesn't mind feeling bored now and then. Others act out and can either be managed in a regular setting with a bit of accomodation (letting them opt out of an abc activity for example), or the school can't provide enough enrichment or accomodation and you get real behavioral problems.
I found dropping in randomly to observe my son's preschool class invaluable, no matter which school it was (he's been to 4 now at 4, 2 have been good and 2 not) I seem to get way more insight that way than by talking to the teachers.
I don't think a private preschool is a crazy thought at all, just depends on what the school offers, if it's a better fit then it's a better fit. At least the preschool age tuitions are somewhat less usually than the regular elementary years.
Take care,
Polly