Welcome to TFP!

It would be great to have another person (in addition to those we already have) validating the chemistry as a cross-check as well as providing new insights.
This is not surprising because bromine is not moderated in its strength by Cyanuric Acid (CYA) so kills algae faster than chlorine with CYA. For green algae this isn't an advantage since chlorine alone at reasonable levels relative to CYA is enough to prevent algae growth (I suspect your FC was too low for your CYA level). For an SWG pool, an FC that is at least 5% of the CYA level should prevent green algae growth. Yellow/mustard algae is more resistant to sanitizers so would need up to double that level to keep it from growing, so usually we recommend eradication by shocking with high chlorine levels, getting behind light niches and under ladders, etc. Sodium bromide to produce bromine will also work, but has side effects I'll talk about below.
Your electrochemical reaction is neglecting to account for the usage/consumption of chlorine which is an acidic process. The net result with a steady-state that maintains an FC level is pH neutral. The rise in pH comes from a combination of carbon dioxide outgassing which is enhanced by the increased aeration from the hydrogen gas bubbles and is also caused by any undissolved chlorine gas that outgasses. See
this post for technical details about the electrochemical reactions AND reactions of usage/consumption of chlorine. By understanding these principles, many SWG pool owners have been able to significantly reduce the rate of pH rise in their pools through methods such as keeping their Total Alkalinity (TA) lower, using sufficiently high CYA levels (usually close to 80 ppm) if the pool is exposed to sunlight, and using 50 ppm Borates for additional pH buffering and mild algae prevention/insurance.
Furthermore, the assumption that higher pH slows down chlorine production is incorrect. The production of chlorine in the SWG is the same at higher pH unless scale starts to form more significantly, which perhaps is what you meant. If you meant that at higher pH there is less of the active form of chlorine, hypochlorous acid, compared to hypochlorite ion, that effect is largely buffered by the presence of CYA as is shown by the graphs in
this post.
Most of the thousands of SWG pool owners on this forum (and other related forums) are able to maintain their pools without getting to the green pool state because they maintain an FC sufficient for their CYA level. The industry recommendation of 1-3 ppm FC is simply too low with their 60-80 ppm CYA recommendation. Prevention is easier (the same is true for the non-SWG pools). When the CYA is high, the use of bromine (from sodium bromide) or the use of a non-chlorine shock (e.g. MPS) or other oxidizer will oxidize algae more quickly and one can also use clarifiers or flocculants, but all of these have side effects. For bromide, you then have a bromine pool, at least for a while. For MPS, it's quite expensive and you increase sulfates. Clarifiers and flocculants don't oxidize or kill so only supplement filtration/vacuuming.
Bromine outgasses. The
Henry's Law constant for hypobromous acid is around 6100 M/atm while for hypochlorous acid it is around 930 M/atm. If there were no CYA in the water then bromine would outgas more slowly than chlorine, but because of CYA the chlorine outgas rate is quite slow (it's actually hypochlorous acid that outgasses in addition to molecular chlorine at pool pH; see
this spreadsheet to see that the HOCl is about 420,000 times higher in concentration than Cl
2(aq) mostly making up for the lower Henry's Law constant for Cl
2 of 0.093 M/atm) and is much slower than the bromine outgas rate since the HOCl concentration is reduced by well over 50 by the CYA so the effective Henry's Law constant relative to FC is more like 46,500 M/atm. Using bromide instead of bromine tabs will have the outgassing go faster because the DMH in bromine tabs behaves somewhat like CYA to chlorine, though doesn't bind to bromine as strongly (though we've never gotten definitive equilibrium constants for that). If one has an ozonator, then ozone oxidizes bromide to bromine and oxidizes bromine to bromate, the latter being an end-point chemical (likewise, ozone also oxidizes chlorine to chlorate).
While the bromine is still in the pool it will tend to break down from sunlight more quickly because none of it is bound to CYA so you may notice a greater demand so need for a higher SWG on-time. Also, bromine smells differently as do bromamines compared to chloramines (say, on your skin when you get out of the water) so your pool may smell different (some don't like the bromine smell). The brominated trihalomethanes (THMs) are mutagenic and increase cancer risk (though it's a very low risk) while the chlorinated THM chloroform does not. Finally, the reason the bromine works is that it is at higher concentration because CYA is not moderating it. This means that it oxidizes swimsuits, skin and hair faster as well, similar to what chlorine does in pools without CYA (unless the FC is very, very low).
As for bromine effects on the SWG cell itself, I have no idea. I suspect it's OK, but don't know for sure. Coatings on SWG cells can be esoteric and therefore finicky.
The
PAN Pesticides Database indicates that Suncoast Stop Yellow is nearly pure sodium bromide. So 4-8 ounces weight per 10,000 gallons would be 3-6 mg/L of sodium bromide for (3-6)*79.904/102.894/2 = 1.16-2.33 ppm Br
2. So this isn't that much so should outgas I would think within a month or so. For comparison, an FC that is at 5% of the CYA level has the same active chlorine level as 0.05 ppm FC with no CYA which is why I referred to the faster oxidation rate of bromine against swimsuits, skin and hair (notwithstanding some bromine vs. chlorine reaction rate differences and reaction selectivity differences).
One clever way you might be able to measure your bromine level separate from your chlorine level is to add a small amount of ammonia to your water sample to convert all bromine to monobromamine (NH
2Br) and all chlorine to monochloramine (NH
2Cl). Except for possible bleed-through from the monochloramine, it should not show up as Free Chlorine (FC) in the test, but monobromamine will show up as FC due to the monobromammonium ion (NH
3Br
+) that may release a highly reactive positively charged bromine ion (Br
+; see
this paper for technical details) that reacts with DPD (and is back-titrated with FAS-DPD). If you have only chlorine, then it should all show up as CC (in the same amount that it would show up as FC if no ammonia were added and if there were no initial CC). Obviously, one needs to use a FAS-DPD test kit to have any reasonable accuracy and should use a 25 ml sample size so each drop represents 0.2 ppm.