I admit measurements of the present make no strong statement about the past, however, within your analogy the flame of a match, after settling down, fluctuates an awful lot on the scale of 10^-15 of its total heat output. But the speed of light does not. Not only would you have to come up with a lot of wild physics to allow c to vary by many orders of magnitude over 6000 y, you’d also have to come up with a mechanism to get it to chill out to the tune of .000000000000001 or less after these quite wild changes. Good luck!
You’re getting hung up on the physical properties of a match in the same way the other poster got hung up on the physical properties of a car. That’s not the point. The point is your very limited human perspective, the tiny window of time you, or men of scientific minds, have had available to you to observe.
And, by the way, I never suggested variations in the speed of light over the last 6000 years.