Thank you for these figures. It's not clear if those are in US$ or Confederate $, but I'll assume the former is more likely (and if accurate, worst case for the Confederacy). What's missing is the interest rates on this debt, which presumably varied between the kinds of debt. Various googlings have produced interest rates of different kinds of debt of somewhere between 3.5 and 8%, depending on the debt. For the sake of a back-of-the-envelope style of calculation I've gone with 6%, but I'm open to a more accurate figure, if known.
If an 1862 scenario (OP, however unlikely that might be), that leaves an interest bill of $27 million per year.
If an 1863 scenario, that leaves an interest bill of $42 million per year.
If an 1864 scenario, that leaves an interest bill of $72 million per year.
For paying that, well, cotton and other agricultural taxes are a big part. Certainly the CSA can claim only part of the value of those exports, but 10% of all agricultural produce (in kind) was the most successful war tax they passed in OTL, so I can see plenty of revenue coming from there - $10-20 million from cotton alone, depending on the level of the tax. Smaller amounts from other agricultural products.
On top of that, there's tariff revenue. The CS Treasury estimated that their (lower than pre-war) 10% tariff would fetch $25 million in its first year, but of course it brought in almost nothing because of the blockade. With peace returning, tariff revenues come with it, and that's probably not a bad ballpark figure. Also some level of tariffs on U.S. goods imported into the CSA (which never happened before). Call it, for the sake of argument, $30 million total.
There will also be some other taxes on top of that, of course, but tariffs and agricultural taxes are going to be the big two. $50 million per year in interest is manageable without crippling the CS economy, unless you think that a 10% tax on agriculture and 10% tariff is going to undo them. (I doubt that, but am open to other views). $100 million per year is going to make things harder. In other words, much depends on the actual interest rate in question, and when independence (somehow) occurs.