I don't agree with many of the things you are asserting.
Most importantly, trying to base carbon dosing on the nitrogen content of foods is just not going to be useful or desirable.
"Carbon can be dosed correctly in aquaculture systems based on the C:N ratio . The food content is known, the growth rate of the target is known, the bacterial protein content in known."
OK, so you tell me. Suppose the foods I am adding to my 100 gallon reef aquarium each day contain 1 gram of total nitrogen.
How much vinegar (acetic acid) dosing each day is optimal?
I gave an example of how carbon is dosed on known parameters in an aquaculture system to prove that autothropic ammonium reduction shifts to heterothropic ammonia reduction by carbon dosing of which you assumed it was not an issue. In an aquaculture system the growth rate of the target specimen and the total nitrogen consumption is known. The protein content of the food is known and protein production due to carbon dosing is known. Carbon is dosed in function to the food added, the nitrogen consumption of the target specimen and the known ammonia production of the target specimen to maintain a high C:N ratio which makes the ammonia reduction ( and the carrying capacity, which is compared to a reef aquarium extremely high) completely heterotrhopic. This is the only way to make the ammonia reduction follow the growth rate in the system as autothropic nitrification by biofilters is to slow for reaching this growth rate and one has not to bother about the nitrate production.
In an aquarium we have to make a choice, keeping the installed mix of ammonia reducers or shift the ammonia reduction to heterothropic reduction. As in an aquarium we have no target specimen of which the daily growth rate and nitrogen consumption is known we can not target a specific C:N ratio. If the choice is made for heterothropic ammonia reduction than the dose is not a problem as long it is enough and is not interrupted. Follow the scheme I would say. This includes that the limiting factor will become the other building materials, in the first place phosphate. If the choice for heterotrophic ammonia reduction is made one can best use bio pellets. ( only for making live easy)
If carbon is dosed correctly on known parameters the bacteria will assimilate ammonia and not nitrate which reduces the nitrification rate producing less nitrate but the denitrification capacity is maintained as long as a nitrate level is maintained. This way the nitrate ( nitrogen) will be removed effectively from the system by denitrification instead of become part of the bio-load. By removing only what is to much a low C:N ratio is maintained. How this is done will answer your question.
The first parameter is the food protein content of which we can estimate ( calculate) the average produced ammonia and ureum secretion after consumption. The second parameter is the daily nitrate overproduction which is easily determined. With the available parameters one can calculate the used amount of nitrogen by the system and to produce this nitrate overproduction. Now we calculate the carbon dose needed to remove the daily overproduction of ammonia. As only ammonia is assimilated the installed denitrification capacity which was insufficient before will now be able to reduce the nitrate stored in the system sending the nitrogen to the atmosphere. The critics will say that nitrogen will be taken up from the atmosphere an cyano's will store nitrogen and release it but cyno's only use free nitrogen when ammonia or nitrate is not available and as long sufficient denitrification is maintained the system will not take up nitrogen from the atmosphere. Anyway, this way I am shore not creating a high C/N ratio which will mess up the complete system balance . As we have some idea about the total nirtrogen input overdosing can be prevented.
For dosing carbon safely one does not need two parameters. Only one, the daily nitrate overproduction. The corresponding ammonia quantity is calculated and a daily carbon dose sufficient to assimilate the amount of ammonia which correspond to the daily nitrate overproduction can be determined. The stored nitrate will be reduced by denitrification. This way overdosing is not possible and nitrogen is removed effectively from the system.
The parameter can also be TAN when TAN is detected in the system, this way correcting an insufficient carrying capacity.