My researcher got back with me:
There are actually three Reports included in the link: images 1-30 are the ‘Battalion-level’ reports. Since we don’t know your grandfather’s Company in the 39th, I decided to exceed our scope of work and located the reports for the two constituent Companies of the 39 Engineers, which were Companies E and F. Pages 31-63 are for Company E of the Battalion; and pages 64-95 are for Company F.
I looked through the reports, but I'm not sure if they are morning reports. One page gives a general idea of what they were doing (training, building a staging area, recreation) and opposite page frequently has names and some notation which I can't understand. I only reports for Sept 1943, which is when the invasion of Salerno happened. My grandpa was a part of that invasion force. His separation papers indicate he is a demolitions specialist. Based on the morning reports and other things I've read on the 39th, I'm beginning to wonder if my grandpa served in a different until and only joined the 643rd for the boat ride home.
Any suggestions of where I should look next? I'm going to start Google-ing demolition specialist, but not optimistic I'll find any but an FBI agent at my door asking about my web searches. :)