Let’s also start talking about what happens when all these infrastructure projects that are being done by the national service kids starts putting the private sector segment of the industry out of business because the pool of slave labor is cheap.
There is no need to de-fund the private sector by a single penny. Every single private sector project can continue as normal. That's the beauty of this proposal. Keep the private sector as is, and put the investment forth in this new, massive labor pool. Because this labor pool is so large and so inexpensive, it can actually shrink the infrastructure deficit, saving America money as shown above, which ends up yielding a return on the investment.
As for the 13A, you very likely wouldn't have a chance of winning in court. "Involuntary servitude" has a specific legal definition which is not 100% in agreement with the definition that you or I might use in conversation. You must have "compulsory labor for the satisfaction of debts or peonage" to meet the legal hurdle of involuntary servitude.