Turner's Navy Gray appears to be of no use as there does not seem to be a complete list of engineering personal, nor did he source his information. Terry Foeander's site gives this count:
http://www.tfoenander.com/csschattahoochee.htm From it I count: 2 Ass't. Engineers, 3 AE's, 1 Fireman 1/c, 4 Fireman 2/c, and 5 Coal Heavers.
Unfortunately, writers concentrated on the deck force personnel and armament with little attention to the Engineering plant. Near as I can tell is that the Chattahoochee had two engines driving propellers and three boilers. The latter I come up with is the reference to three furnaces on page 87.