To be clear, I am disputing two points:
1. that the minimal speed is an inherent limitation in any system of producing consciousness.
2. that consciousness is some process distinct from information processing.
The burden of proof is on you to show evidence for either of these conjectures, and I for one am not convinced by the study you cite and your attempts to wrangle a handful of others into the mix. In the edifice of scientific research on consciousness, your claims are the extraordinary ones.
Are you kidding me?
What more evidence can I possibly provide?
Regarding #2, I'm not saying that you can't put the IP label on the process of generating conscious experience. Obviously, you can. But so what?
I can put the "cell functioning" label on the process of DNA replication, along with everything else a cell does. That doesn't mean that it's not a distinct function with specialized processes and structures to handle it, and that if we want to discuss the construction of an artificial cell, and the effect that tweaks to that artificial cell will have on the process of DNA replication, we can somehow ignore dealing with those processes and structures.
Sure, you can call the generation of conscious awareness "information processing". And in doing so, you've accomplished zip.
The fact is, all evidence -- which I've already cited, but I can't tell that you've read -- demonstrates that the function of generating consciousness relies on a particular set of physiological functions, and that it is distinct from (but of course connected with) non-conscious processes.
Which brings us to 1.
The most recent research shows that the processing of input which is made available to conscious experience, in contrast with the processing of input which is not, is marked by a sustained and coherent brain-wide coordination of pre-processed data in real time.
That being the case, and together with the cinematic model of conscious awareness which is supported by numerous studies (on subliminal thresholds, blind sight, simultaneity thresholds, etc.) it is reasonable to conclude that spacing the brain's neuronal firings too widely in time will result in a loss of cohesion that will make the ignition and maintenance of the necessary processes for conscious awareness unsustainable.
It is roughly analogous to the failure of a computer to play a DVD if the operating speed is slowed down too much.
Now, there may be other ways to generate consciousness, but so far, nobody knows of any.
So if you're going to speculate that our hypothetical robot has a brain which is conscious by some means as yet unknown and unimagined, the question of what happens when you slow its operating speed is unanswerable.
Therefore it is ludicrous to attempt to assert that the robot will remain conscious when the operating speed is slowed down drastically.
The best we can say is that if it uses a method analogous to the brain's method for producing consciousness, a drastic slowdown will likely result in insufficient data coherence in real time for consciousness to be maintained, and if it uses some other method then there's no way to even speculate what the effect will be.