Here's the gist of my answer:
- Some physicists have been working for decades on theories involving a variable speed of light.
- These theories are not widely accepted within the physics community.
- Empirical measurements have placed strict constraints on some of the predictions.
- Even if the theories are correct, there's only significant change in the speed of light over billions of years, and in the early universe - not in the last 6000 years.
Therefore, the answer to your question is a no.
A theoretical introduction: variable speed of light theories
The creationists have stumbled into an issue that has proved to be a slight problem in physics. For several decades, a few scientists have worked to set up consistent theoretical frameworks involving a speed of light that varies in time, originally motivated to avoid the issue of cosmological inflation and related issues, which are now a bit better understood. Many of these variable speed of light (VSL) theories are extensions of general relativity. See an article by Magueijo for more; I mention it here only because Magueijo is one of the major proponents today in VSL theories. I believe one of the latest major papers in this vein is Afshordi & Magueijo 2016.
The problem with applying VSL theories to the present case is that these ideas arose to explain phenomena in the earliest stages of the universe - not the last few centuries. As such, predictions being derived are rather cosmological in scale, and Afshordi and Magueijo are much more interested in checking variations in the cosmic microwave background than phenomena in our astronomical backyard. The point of this is that some - some - physicists - have been working on these ideas for decades, but not in the direction these creationists are trying to go.
Just before posting this answer, I noticed that one of your articles mentions Magueijo, as supposed evidence that the creationists' theories are viable. They're not (see the next section), because even Magueijo's theory, which is pretty far out on the fringe, doesn't predict the effects they're looking for.
Back to experiments
In recent years, we've had excellent cosmological measurements, primarily thanks to the WMAP and Planck satellites. Qi et al. 2014 (arXiv version) use these to attempt to constrain VSL theories as well as possible. They make the assumption that the speed of light varies as a power law with a, the scale factor of the universe, which describes the size of the universe as a function of time; this in turn means that c varies with redshift, and thus time. Using this form of c(t), they fit the free parameters (chiefly, the index n) to calculate quantities relating to Type Ia supernovae (a common cosmological tool), the cosmic microwave background, the Hubble constant, and something called baryon acoustic oscillations. Qi et al. they came to several conclusions:
- The index n = -0.0033.
- At redshifts less than z ~ 0.1 (which corresponds to a lookback time of over 1 billion years), the variation in c is essentially zero.
- Even at redshifts up to z ~ 10-100, the variation in c is less than about one part in 100.
The fine-structure constant
Physicists have also been interested in determining whether a variety of other physical constants are in fact constant in time. One key target is a quantity called the fine-structure constant, α, so called because secondary "fine" splitting of energy levels in the hydrogen atom are proportional to the constant squared. Understanding whether α is truly constant is important because even small variations in it could have catastrophic effects. What's important here is that the fine-structure constant depends on the speed of light, and variation in α could indicate variation in c.
Some of the earliest - and possibly the most famous - measurements in the change in α - involved the natural fission reactor in Oklo, Gabon. A variety of studies found the fine-structure constant changing by as little as one part in 1017 per year (see Uzan 2002 (arXiv version) for a review) at present. Other geological results, typically involving alpha and beta decay, have produced upper limits a few orders of magnitude higher, but still quite low. As these studies give us limits applicable on geologic timescales, they show that α certainly could not have varied much over the past 6000 years; ergo, unless the other constants that make up α (the elementary change and Planck's constant) have also been changing, the speed of light cannot have changed significantly over the same timescales.
(Though it's not strictly related to the claim because it involves going much further back in time, we also have astronomical and cosmological constraints on the variation in α; see again Uzan 2002. By studying spectral line splitting in quasar spectra, this variation has been explicitly calculated up to redshifts of z ~ 2-3, rather than the mere placement of upper bounds. Assuming certain systematic errors are not at play, this could be significant; however, there seems to be conflict with various geological results. At any rate, these are not widely accepted as definitive evidence of any variation, and certainly not of a recent one.)
Putting all of the above together, the creationists' claims - which require enormous variations in the speed of light over recent timescales - seem to be ruled out completely, even if smaller variations in c or α cannot be ruled out farther back in time. Even if the fringe science they cite is correct, it still doesn't support their claims.
The Setterfield-Norman paper
I read a paper by Setterfield and Norman from 1987 that was responsible for some of this mess. I noticed several problems with their analysis:
- Some of their data is grouped together, and presented as if they were all taken in one year - the mean of the actual years of data collection. It's unclear if this is also used in the fitting.
- The functions they attempt to fit the data to are poorly presented. r2 values are missing from three fits, and at least two of the nine fits show a monotonically increasing speed of light - not a decreasing one.
- Three fits have r2 values similar to within one part in 104, which is suspicious. The choices of functions to fit are not explained (and look quite bizarre), leading me to believe that ones leading to fits that did not agree with the authors' conclusions were omitted.
- Table 22 shows a) both a decrease in the measured decay rate as one reaches the present, The authors interpret the decrease in decay rate as implying that the decay is slowing; most of us would interpret that as showing that there simply is no decay.
- Finally, it's not clear that a valid statistical analysis was undertaken, or that r2 is the right value to be relying on here. They claim to reject hypotheses of constant speed of light, but in many cases by percentages that are less than 3 sigma, and very much below the standard of proof for a discovery.