they would reappear at different intervals. ... What do you think?

Let's see. How are you measuring the intervals?

if your hypothesis that photons are constantly accelerating is correct

I'm not sure that is the hypothesis -- mine or anyone else's. That is to say; I'm not sure that "The SoL is not constant" (Or "The SoL is (and has been) constantly [sic] increasing since the Big Bang; is the same as saying "photons are constantly accelerating".

The problem starts with understanding that whole thing about the 'expanding universe'. People generally get that all the galaxies have their own motion, relative to us and everything else. And headline "they are all moving away from each other" is taken as read by most of us.

The tricky bit that goes over a lot of peoples heads, especially science correspondents and other media types, but the rest of us, including some you'd think would know better, is the fact that the reason, and indeed the only way for all the galaxies to be moving apart from all the other galaxies (in the large), is if the universe itself is actually getting constantly bigger. The very fabric of space-time is increasing. Space itself is accruing more space.

The favorite demonstration of this is dots drawn on a semi-inflated balloon. You blow the balloon some more and all the dots move apart from each other. The problem with that demonstration that is glossed over, is that the dots themselves also get bigger, so the relative distances between them stay proportionally the same.

It's like the unit of distance increased. Although we as outside observers of the system (the balloon the dots and the distances between them) can perceive the change, if the were some (tiny; the relative size of humans to the universe) living creatures on the surface of the balloon, then they wouldn't be able to perceive the change because their rulers, and indeed themselves, along with everything would also increase in size, so everything would appear to be exactly the same.

Which brings me back to the both the description of the hypothesis and your proposal for testing it.

If space started as a singularity, an infinitesimally small point of nothingness; and has grown to its current measured observed size over 13.8 billion years, and the speed of light has be constant and the same constant right from the beginning, then we have a measure -- and a stupidly large number 130558080521615040000000000m -- for the size.

If however, the SoL started at zero 13.8 billion years ago (that becomes questionable under this scenario; but I need a number here), and has reached it current speed now, then the rate of that acceleration is Δs / Δt = 299792458 / 130558080521615040000000000 = 2.2962382473934021910889055687635e-18 m/s², so tiny that even if we had units of time and distance that were not tied to the SoL; it would require there be decades (if not centuries) between observations, before the change would be sufficient for our best atomic clocks to detect.

And finally, the basis of the experiment you propose is (I think) that because older things are further away, the light arriving to us must have started out more slowly than 'new light' from close by, and thus the two must be traveling at a different speeds; but that isn't so. If the SoL itself is accelerating, rather than the photons we measure in terms of it, then all light, new or old, near or far, would, at any given moment in time be traveling at the same speed -- the SoL. It's just a different SoL today than it was a century, or millennia, or a second, ago.

And if you accept the indivisibility of space & time; that they are aspects of the same thing as General Relativity suggests, and space is, and has been expanding since 'the beginning'; and the thing that links the two is the constant c; then doesn't that mean that time -- as in the length of one second or one day; not the totality of seconds or days since the BB -- must also be expanding. It would be the only way for the constant to remain constant.

But the problem with time changing is that we have artifacts going back 5 or 6 thousand years Ancient Egypt, Sumerian, Inca, Maya, that record time in physical objects; with sufficient accuracy that we can wind back the clock and align them with celestial bodies in their positions then -- by sight; no units of measure tied to SoL to mess with things -- and they line up. And those thousands of years are sufficiently long that if time were moving at a different rate, it would show up.

So if space is expanding and time is constant; then the only thing left to account for the variance is c.

Now I need to switch my brain off before I go mad :)