My take is that a photograph is inherently a capture of a moment in time. Dodging and burning, contrast masking, saturation, etc, doesn't change this. It's still about a moment in time. When you blend multiple exposures (rather than different raw conversions from the same exposure) you're creating a digital composite. It's no longer a photograph; the photographs are inputs to the composite. Like newspapers used in a collage, it's no longer a newspaper. The act of compositing creates a new, inherently different, type of work.
Painting is also a completely different type of work - even a courtroom sketch artist makes no claim to be producing a photograph. It's a sketch, and exactly what you see very likely never happened.
That said, I enjoy making digital composites and shoot to produce material for it (I shoot medium format digital on Mamiya 645) just like I typically like to present most of my photographs as non-composites. Their expressive power is different. They are inherently different, with different emotional response - and I see this as a good thing.
This is obviously a contentious issue - and a true definition of whether HDR is photography or something else is not yet upon us. However, I think it's worthwhile pointing out another type of photography that uses 'composites' and therefore shouldn't be (by your definition) called 'photographs'. That is, astrophotography - where to create a single image, photographers (or should I say, composite artists?) combine a number of exposures together to create their images.
As for my own opinion, I say that both HDR and astrophotography are types (or methods) of photography. However, a lot of what is being done with HDR is designed to
deliberately make the image look more like a painting than a photograph. In which case I tend to think of these as 'digital artworks'.
The reason I'm okay with HDR being considered photography is because I don't adhere to the definition of photography being 'a moment in time' (there are too many multiple exposure photos to list, but
here's a classic), but more of a reference to the media used (I've been an applied media art student for the last year - most definitions come down to the media used or what it is going to be used for). Also, when I think about it, some of my HDR shots have been made up of three images, totalling a period of maybe 10-15 seconds in time. This is, in many respects, more of a 'moment in time' than say, a 30 second single exposure.
In film photography, there are different types of film that each have different sized dynamic ranges. Different brands also, have different dynamic ranges. To me, HDR is essentially creating a 'film' which has a very very large dynamic range.
Here's a couple of images - the one on the left is HDR, the one on the right is the original exposure from the camera - tweaked with shadows/highlights, etc in Photoshop.