Wouldn't this mean that the speed of light is slowing down?
Probably yes. But only in relation to the accelerating clock. When compared to a hypothetical clock that is not speeding up, it would remain constant.
If time is accelerating won't that invalidate your math?
Probably yes. Working on that--but I think the math would still be approximately correct, and it's already an approximation anyways. Mostly, I want to spend my energies developing and conducting the experiment, see if there is any measurable time-rate-increase, and then go from there.
What about other evidence that supports the big bang theory besides redshift?
I'm not an expert on cosmology. But to the best of my knowledge, there is no direct evidence proving that time doesn't slowly accelerate. There are observed phenomena that support an expanding universe besides redshift (such as Cosmological Background Radiation (CMBR), and the concentration of primordial elements), but the bridge between observed results and conclusions is theory, and all theories that I know of have the unstated assumption that time is not accelerating. A theoretical accelerating clock is a tricky thing to account for and frankly, the idea makes my head hurt. But I think we can test for it with experiment and rule it in or out. On the plus side, an accelerating Universal clock would tie time to something (right now it's tied to nothing and people argue of its very existence). Also, it's existence may solve some of the "mysteries" associated with Big Bang Theory such as dark energy, dark matter, the horizon problem, the lack of observed magnetic monopoles, and the flatness problem. For more information visit:
https://en.wikipedia.org/wiki/Big_Bang