Ok I'l give you a couple examples to show you that this is anything but hair splitting as the differences in carbonation speed are really significant.I dont know what hairs your trying to split here
You mention your maturation vessels only allow you to apply 15 PSI of pressure. Let's say you target 2.5 vols of CO2 in your finished beer.
Now you could achieve this in two ways using the set and forget method:
1 - Chill to 32°F and apply 8.1 PSI
2- Chill to 54°F and apply maximum pressure of 15 PSI
In both cases you'll reach your desired carbonation level. In the first case you'll be limited by the cooling capabilites (I'm assuming 32°F will be the lowest temp you can reach in practice) in the second case you'll be limited by your vessel's maximum working pressure.
I can't calculate how long it will actually take to carbonate as I'd need to know all the variables of your setup but I can do a differential calculation. Let's say it takes exactly 10 days to reach carbonation at 45°F. At 32°F it'll take you 12.94 days or nearly 30% longer. Now that might not be a problem for your operation if you're demand-limited and working below maximum production capacity, but if the opposite were true then those 3 days you'd save would certainly work towards increasing your margin, wouldn't you agree?
Now let's assume your equipment allowed you apply up to 30 PSI of pressure, which is certainly the case with corny kegs. The comparison now is between:
1 - Chill to 32°F and apply 8.1 PSI
2 - Chill to 65°F (or don't chill if that's your ambient temp = energy saving!) and apply 29 PSI
Both settings will let you again reach 2.5 vols of CO2 using the set-and-forget methodology. In this case if it would take you 10 days at 65°F to reach carbonation dropping the temperature to 32°F would increase your process duration to a whopping 18.33 days or over 80% more. I'd say that would definitely have a positive effect on your costs and therefore your margin which as a commercial brewer I'm sure you'd be very happy about, am I right?
Now if somebody asked you if it would be faster to carb his freshly kegged ale at room temp or if he should chill it first and then carbonate using set-and-forget and assuming he is not equipment-limited in any form or fashion, based on the above what would you think you should tell them?