Here are some of the raw numbers:
Your comments about the timing of these expenditures may be somewhat correct, since doubtless "fiscal year 1862" began sometime in 1861.
I’m sure you’re right. No way actual spending during the calendar year 1861 went down as a percent of GDP.!
Massive federal spending started to ramp up in May and continued accelerating through the rest of that year. Although much of the initial expense was paid by the states, possibly with later reimbursement by the feds.
I note your numbers show GDP doubling in three years. You will excuse me if I take that with a grain of salt. Especially when a very large part of the 1860 economy was no longer part of the equation.
During the equivalent period of WWII GDP increased only by about 50%.
I believe at that time the Federal fiscal year ran from July 1 to June 30.