From: Sant Pere de Ribes, Spain
For the Basic Rules (or any rules in which "Advanced Buildings" is turned OFF), the USA and CSA will have constant levels of reinforcements -- presently the numbers are 20,000 for the USA and 10,000 for the CSA, but these numbers will be moddable in the Data\AcwConstants.txt file. The "Invalid Corps" upgrade will modify this number, just as it modifies reinforcements in the advanced rules.
These numbers are based on data that the USA had about 2,500,000 men during the war and the CSA about 1,250,000. The Civil War lasted about 48 months, or 96 of our turns, so this gives almost 2M US troops and almost 1M CS troops, and assuming that the player starts with a few hundred thousand and recruits/requisitions a few hundred thousand more, gives approximate historical totals (the historical numbers include some troops out West that aren't on our map). The numbers are comparable to what players can get from Camps in the Advanced game -- though in the Advanced game (depending on the other options) it can take a while to build the 20-30 additional camps required to get this level of reinforcements, it is also possible in the Advanced game to get more reinforcements than this from more Camps.
I considered briefly modifying these numbers by things like National Will, but since this rule will be for the Basic Game I'd like to keep it as simple as possible.
Your argument seems right that the US should recruit about 20,000 per turn and the CS about 10,000. But you seem to be proposing to direct all these recruits into existing regiments, whereas in reality most of them (88% of them in the case of the US in 1862) went to form new regiments.
Also, it strains credibility a bit to imagine the CS maintaining the same constant rate of recruitment into 1865, with a lot of its original territory captured or inaccessible. I think the loss of territory may be even more significant than the National Will factor.