I've seen them fly much higher than 40 feet, so there's definitely no magical anti-firebird fly swatter up there just waiting for one to crack the 40-foot ceiling

Then again, you are in the UK, and laws may be different over there...
If the plane is box-stock, the CG should be fine. It sounds like the plane is trimmed out okay, too, if you're cruising level at half throttle. I suspect that it's just piloting skill that's necessary here. Jamming the stick to full throttle will generally cause Firebirds to pitch up sharply and stall. That's because they don't have enough power to sustain a vertical climb. Try applying the throttle graudally.