You have a long target so the angle of scattering into the HRS from one side is smaller then the other. To first order the answer to your question as to why you see more events from one side of the target then the other is just the Mott cross section has a strong angle dependence. Also note y is in spectrometer frame (see page 341 of the Hall A NIM paper) and that positive y for the left arm is looking at negative z.
If I am doing my geometry correctly (before having my morning coffee) the change is several degrees from edge to edge to a point acceptance one meter away. Using the 20.5 central angle (that I wanted to use) I got 18.6 to 22.7 degree range. Also note that HRS isn't a point acceptance, but has over a degree bit for each of these edges, so full range for this kinematics and this target length is more like 17.5 to 23.5.