Weddings pay consistently, wildlife usually don't. So, if it were me, my priorities would be on my paying customers. I'd get the 70-200. It's really not long enough for a lot of wildlife shots, I'm sure you know (tho I have shot a bull elk with a 17-35mm once... I don't recommend it).
However, if the book project also is a potential income source (maybe a less certain one than the weddings?), it's more of a quandry...
Maybe you should once again rent something for the wildlife shots... or add a longer, used lens at some point. Or buy a lens for the project and then sell it when done.
Canon 100-400 IS is about $1600-1700, last time I looked. You might want to check out the Sigma 120-400 OS (around $1000) or 150-500 OS (approx. $1100), or look for one of these used.
Canon 400/5.6 used might be a more affordable option. But it lacks IS, so figure on a tripod or at least a monopod some of the time.
New the Canon 300/4 IS is more expensive than either of the Sigma zooms, but somewhat less if bought used. Combine it with a 1.4X teleconverter to have two very useful focal lengths out of one lens. The Canon 1.4X Mark II or III or the Kenko Pro 300 1.4X DGX are all good options for use with that lens.
Note: 70-200 + a 1.4X might be tempting... but still comes up short for a lot of wildlife. 70-200 + 2X doesn't play together well... no AF with an f4 lens on most Canon bodies, and too much loss of image quality on all but the most expensive combo (70-200/2.8 IS Mark II and 2X Mark III.)
In your situation, I'd probably go with the 70-200 first.... then figure out a way to cover the cost of the wildlife lens later. There isn't a single lens that will do it all.