The issues are a little different depending whether you are photographing or scanning. Large flat bed scanners are expensive, but you could resell after the project:
As for photographing: I prefer flash over continuous, but once you have the lights set up to give an even light field, there should be little difference. And which ever way, shoot tethered.
Generally you donít need more than two lights except for larger pieces, certainly much larger than you have. Art repro lighting is well known: two lights equidistant, equiangular, identical and at the same power output, usually around 45ļ to the work. Meter the corners and centre and go for less than 1/10 stop difference, which is about the best that most meters can measure. Without a meter you can shoot a plain sheet or large gray card and examine it in whatever software you are tethered to.
The real problem is the binding. I have at times unbound books, and had them professionally rebound after. If images are too close to the gutter (the margin nearest the binding), or worse, as in your case, centre folds, then things are much more difficult.
I use heavy glass to flatten pages, or plexi with weight bags. Various thickness shims to keep the pages level.
Shoot a test target (GretagMacBeth ColorChecker or such) at the start, end, and intermittently during the process. And even so, it is good to have the originals with you for reference while post processing.
Shoot raw and use the largest space and highest bit depth available.