Stephen Jay Gould (a more rounded intellectual than Dawkins on these issues) rightly called culture "the Lamarckian juggernaut" because of the pace of change and the ability to adjust, or in the terms of Lamarck "the inheritance of acquired characteristics."
I'm extremely sceptical about the idea that the pace of cultural evolution is fast because it is "Lamarckian". The most obvious hypothesis to account for the speed of cultural evolution is that ideas reproduce rapidly between brains, reproduce rapidly within brains, and are themselves the product of evolving signals in axons and dendrites, which reproduce at a lightning pace. So: incredibly short generation times (plus fairly impressive parallelism) accounts for most of cultural evolution's rapid pace.
As far as I can tell, most other attempts to account for the pace of cultural evolution don't fully account for the force of this point.
Anyway, I see no easy way forwards on this issue - short of a quantitative analysis. The rapid generation times and high parallelism of evolution inside brains can - in principle - be measured and compared with systems based on DNA - such as viruses and bacteria. I don't expect dramatic differences in evolutionary rates (however measured) per generation in systems with comparable parallelism. Intelligent design mostly speeds up evolution to the extent that it represents a high-speed parallel copying processes with short generation times. I think this is the most obvious null hypothesis for explaining the rate of cultural evolution. It's the baseline from which other hypotheses need to differentiate themselves.