Not sure what you're saying, or seeing here.
Assuming the time-stamp is within about an hour for both charts (La Porte IN, UTC -5). The Sun/Moon position chart is showing the moon roughly mid-Pacific. The mid-Pacific (let's say the International Date Line) is about 90deg west of Indiana, which is going to put the Moon's apparent elevation roundabout the horizon, which corresponds with the Moonset Chart; 5 deg.
It's on a similar latitude but, because your eye-line is following more-or-less a Great Circle, that is going to appear to be north from due west, hence moon direction of 297deg seems plausible.
By a coincidence it was a bright sunny day here in my UK town and around 11.00am (UTC) the mrs pointed out that the moon was still visible. It was roughly 20deg above a prominent local mountain which is NNW from here. (edit; sorry, WNW, about 300deg).