[Overdrive]

jaykay is correct about the manual deployment of the spoiler. Once you press that switch the spoiler will stay up until you either manually stow it or until the car is powered off and started again, at which point it resumes normal operation.
When you start the car, does the spoiler warning light come on and stay on until you start driving (like it's supposed to)? That'd tell you if the bulb burned out if you don't see it upon starting the car. This culprit is not very likely, but you never know, so check it out. Clearly the speeds you're getting to at this point should see the spoiler out doing its job, but unfortunately we can't see that from the driver's seat.

I do wonder about that GT3 nose...maybe it's providing more downforce on the front to the point where the downforce the stock rear spoiler puts down is no longer sufficient. Maybe you should see about getting an Aerokit-style permanent spoiler to put on the back, or if you don't want to drill your trunk lid (understandable), if you still have your original nose, maybe throw it back on and see if the car settles down?

I know Lime Rock Park's never really been one of the smoothest tracks out there, even after the repaving not long ago. Is the road surface where you're encountering this any sort of bumpy? It could be the line you're choosing has a spot that the chassis doesn't like, and gets that reaction from it.