We waited until we had to test. By that I mean we waited until the results would immediately open a door, change something in their current setting or provide input into making a major decision. For DS we still ended up having to test twice because his first results at 6.5 weren't conclusive for his LD. His WISC scores were quite different as well likely because he wasn't the most cooperative kid the first time around.
Many schools around here want recent results and will totally ignore any testing older than 2 years. I suspect they would be even more likely to ignore it when dealing with a very young child or if it suits their agenda (as in they are highly resistant to early entrance and will then use that as an excuse). If you think that early entrance to K will be a help and that requires some sort of proof then I would aim to test shortly before you need to apply.
I will also add that in our experience we had less issues with play based curriculum than we did once the kids entered more traditional classrooms. At the end of the day it really boils down to the teachers and if you are lucky enough to have peer for you child (you hint that the center now deals with several similar children which could make a big difference). If that happens to be in the preschool and the teachers are wiling to keep up then a 3rd year there might even be better than an average K classroom. Hard to say.
