Reading through all of this and testing out your demo I have a hard time believing it is the GPU causing these frame drops/bad performance etc.
I would say I have a rather Middle-End PC:
AMD X6 1090T 3.8GhZ
8GB DDR3 RAM
2x AMD HD6870
I've tested the demo in firefox/chrome and it barely got stable 60fps, with frame drops down to 48fps and an average fps of around 55.
In my opinion it can't be a GPU problem if I get these values, but rather a case of maybe bad CPU optimisation? (As one core was used around 100% during testing)
Don't get me wrong you've probably optimised it as best as you could, but for example my game SoW which is rendered in 1080p with downscaling of some assets etc. has a by far more stable performance (60fps fluid) on my machine and on a laptop with something like 2x 1.8GhZ and an Intel HD3000 where I got around 20-30fps.
Additionally to that, the fact that you get better performance with Canvas2D is quite shocking, because when I tested SoW with Canvas2D I barely got around 10fps on my pc
Quite weird the whole case, I'll just follow this case and see if I may get an idea at some point as to why it happens.