What's the problem with this 1967 Barracuda trunk trim???

The issue is that the trunk lid is from a 68. You are correct that the holes in the middle are for emblem attachment. The holes for the upper and lower trim for a 67 are along the lip edges, as well as additional holes to mount the center piece all through the center area. This is difficult to modify as access to the mounting nuts is from inside the trunk. Your best bet is to locate a 67 decklid and trim.

Swapping to 68 taillights is an option, but as the reverse light makes up the outer section you will probably not have it light up as 67 & 69 have the reverse lights on the lower valence. 68 does not