I truly tried to find data to support your claims.
"My claim" isn't unique, or really even mine:
Don't chase pH.
You may be looking too hard if you aren't finding anything. Check out the articles section here on R2R:
Beginner Topic Why Chasing pH is a Trap for Beginner Reefkeepers
If you want to know why *we* might care about pH, Randy's more recent article says it very well:
pH And The Reef Aquarium (2019; the discussion section veers into "my claim" as early as
post #3)
I can say I've tried to do my part as a volunteer to spread the knowledge. (* here, on nano-reef, and on reefsuccess.com which is also in the sig of every post I make)
There's a usable search function on my site to look for a term like CO2. (I recommend looking at everything in the linked search.) Let me know if you still don't find what you're looking for.
There are too many good articles on the subject of
basic reef tank chemistry by Randy and others to even try to address that in someone's thread. Here is one great one:
Reef Aquarium Water Parameters
Numerous peer-reviewed studies have shown that:
-High CO2 impairs coral growth and skeletal formation.
-Low pH stresses corals and can even dissolve their skeletons.
-Stable pH (typically 8.1–8.4) is critical for coral health in reef aquariums.
This is not the current state of knowledge. Multiple journal articles you can find on that reefsuccess.com search will clear this up.
But here are a couple of shortcuts:
First, we've known since at least 2009 that corals have an incredible ability (tho not unlimited) to deal with changes in water quality around them.
The authors combine a lot of this information and
test the limits of what corals can tolerate here:
Why Corals Care About Ocean Acidification: Uncovering the Mechanism (2009)
Last, skeleton formation was found to be independent of pH in 2017:
https://reefsuccess.com/2017/08/10/biological-control-of-aragonite-formation-in-stony-corals/
Both of those ought to be

for anyone who hasn't bumped into this information yet....keeping in mind that our corals don't have the same limitations as corals in the ocean.
One key quote for our thread from the 2017 article:
Last, our results strongly suggest that the ability of corals to calcify is biologically controlled and thus relatively robust. As such, the biological reaction is far from thermodynamic equilibrium, and, hence, biomineralization in stony corals is not simply related to physicochemical parameters such as the equilibrium saturation state of carbonate ions or the bulk pH of seawater (
33).
Skeletal density and growth rate are two common refrains on the topic...things which have been found to be "affected by low pH". (HINT: The tests in these articles were not good simulations of a tank environment; that wasn't part of their testing.)
Do less-massive skeletons automatically mean "unhealthy"?
No. Corals reproduce sexually AND vegetatively. A less dense skeleton makes natural fragging more likely. It is a life strategy under historically-predictable circumstances for them. (CO2 levels have historically been both much higher and much lower than today through the history of corals....through the current lives of some of the older corals out there!)
Does slower growth automatically mean "unhealthy"?
No. It might be surprising, but faster growth is actually associated with lower fitness factors such as slower wound healing.
What makes some of these studies I've linked especially of note is that some take care to implement a few of the controls we as aquarists (reefkeepers!) would use to keep corals healthy – eg feeding and NO3/PO4 dosing – and they see the same positive results we see.
Their positive results in the 2009 article reminded me of the findings in this 2018 posting:
https://reefsuccess.com/2018/08/27/...-ultrastructure-of-symbiotic-dinoflagellates/
@P-Dub, the truth is that folks make LOTS of assumptions about whether their corals are "happy" or "unhappy". Most of it is very unscientific. And in some cases what used to be thought correct turns out to have a different story. As it turns out, corals (and other calcium precipitators like clams and snails) have the proper "gearing" to deal with the up's ad down's associated with oceanic levels of pH....it's not something they worry about.
@Skunk_Works, we are unfortunately glossing over the human health angle just to dwell on the (in)validity of chasing pH numbers.
At high enough CO2 levels to cause anything that could be considered "a pH problem" in a reef tank – look again Randy's chart I pasted into
post #8 – either CO2 or alkalinity would have to be pretty drastically off.
To get your reported pH of 7.7 to 7.8, alkalinity could have cratered to under 0.75 meq/L (< 2 dKH) on the chart – but it doesn't seem like there's any current suspicion of a drastic alkalinity issue.
Looking again at the chart in post #8, even 700 ppm CO2 will only drop the equilibrium point of seawater to 7.95 or so; not THAT far from 8.1.
*** Atmospheric CO2 being in excess (≥1000 ppm) needs to be ruled out IMO.
Please start with Randy's aeration test.
The numbers need confirming (eg with a CO2 monitor) but numbers like these point to a CO2 concentration four digits long. If you are unfamiliar, look up the effects of 1000 ppm and 2000 ppm CO2 on human health and sleep. It's only a benefit if you're photosynthetic!
In case it's not a household issue,
good ventilation is crucial in the room where the tank is as well as the house. So don't keep the fish room too sealed up. In the old days, all houses had "good ventilation" whether it was desired or not. Modern building methods can cause CO2 to build up though.
If you do confirm excessive CO2 but there are no simple remedies like opening the room more, consider getting a professional opinion on changing your HVAC setup. It could be just an adjustment, or it could be some new equipment....totally depends on your actual situation. Treating just the tank in this situation (ie CO2 > 1000 ppm) is unproductive and unwise.