Let's see how much that constant would have to change for a young Earth.
90 percent change - Earth is 450 million years old.
99 percent change - Earth is 45 million years old.
99.99 percent - Earth is 4.5 million years old.
99.999 percent - Earth is 450,000 years old.
99.9999 percent - Earth is 45,000 years old.
So in other words, the rate of fluctuation in radiometric decay would have to be greater than 99.9999 percent to get to a 6,000 year old Earth.
If that were the only way to generate the observed patterns, you would be right. (Actually, acceleration of decay rate up to 10^14 power has been measured, but under exotic conditions I don't think are directly relevant - see http://www.answersingenesis.org/tj/v15/i2/acceleration.asp.)
So how can we explain 'dates' of 50, 60 kya and so on, in a 6000 year timeframe? Not through accelerated isotopic decay in the case of C-14. Instead it is the inevitable result of the Cataclysm.
Think about it - we believe coal and oil reserves, the vast majority of fossil deposits and so on, were buried ~5,000 years ago. What sort of C12/C14 ratio would we expect prior to this point? If there were 64 times more biomass before the Cataclysm (which is in the ballpark of estimates I've seen), that works out to 2^6 times as much C12 in the biosphere. In other words, C14 would have been diluted amongst much more C12, creating the illusion of 6 half-lives to anyone measuring a sample after the Cataclysm.
Moreover, let's assume the most radical case that the earth was created with no C14 inventory. In this case any life dying early on would have had an even smaller C14/C12 ratio, creating a much 'older' apparent age (per uniformitarian dating assumptions). A few years would telescope out to multiple apparent half-lives as the C14 inventory increased from cosmic radiation.
We can test who has the right model very easily: if the earth is billions of years old then dead carbon samples from coal, diamonds, etc. should have zero C14 in them. (If the entire earth were composed of C14, with a half-life of 5730 years there should not be one atom left after 1 million years.) Whereas on a young earth there should still be some measurable C-14 among deposits dating from the Cataclysm, even given the dilution effect of the original C12 inventory.
You can study this on your own, but here are some articles with the results:
http://www.answersingenesis.org/get-answers#/topic/radiometric-dating
The reality, as folks in the radiocarbon field have known for decades, is that everything they measure has significant C-14. The results are too consistent to be contamination, and contamination is not a reasonable explanation for things like the C-14 measurements of diamonds, whose structure presumably rules out contamination as a risk. Creationists have had a field day measuring coal, carbon deposits associated with dinosaurs, and so on. None of this should be measurable if the conventional model were true.
In the new model, recent (say less than 3,000 years) results from C-14 are pretty much the same as before. Beyond that the results start to telescope more and more strongly. A conventional C-14 date of 4,000 years might translate into a real date of something like 3,800 years, whereas a conventional date of 25,000 years might telescope down to 5,000 real years. It depends on the exact calibration curve and the usual issues (attendant to all models) regarding potential anomalies in carbon source material and so on.
You can make other predictions between the two models as well. For example, on a young earth with a low initial C14 inventory, we would not yet have reached an equilibrium condition with as much C14 being created by cosmic radiation as is lost from decay each year. On an old earth the production and decay of C14 should have long ago reached equilibrium. Insofar as C14 is produced by cosmic radiation, only fairly radical changes in solar output (with profound implications for life on earth) would cause a disjoint in the production/decay ratio, and it would immediately begin smoothing itself out after any such event.