In somewhat-analogous circumstances almost 30 years ago, a court said "no." The case was Micro-Sparc, Inc. v. Amtype Corp., 592 F.Supp. 33, 34-35, 223 USPQ (BNA) 1210 (D. Mass. 1984). The defendant offered a keyboarding service: It typed in the source code of programs published in a hobbyist magazine, then sold disks to purchasers of the magazine. The court rejected a fair-use defense and held that this infringed the copyright in the programs. (Adapted from a chapter in a treatise I published long ago.)
That the subject was a computer program is what seemed to trip up the case in my opinion.
So for your scheme to work accurately they'd have to try to keep track of that.
I think it's too risky, and would go with "scan the exact book in."