Others may have different opinions, but I don't know that a dedicated year off to "make connections" will help you that much. You should speak with your current research mentors and map out a plan of attack for your residency application.

To answer your other question, most residency programs generally set a Step 1 cutoff to get their stack of ERAS applications down to a reasonable number to send off to reviewers. This cutoff is going to vary from program to program, but I have heard anywhere between between 235 and 250. Obviously, the more competitive programs will have higher Step 1 cutoffs, and they might use additional screening criteria (i.e. honors in surgery and medicine, AOA). If you rotate at a particular program, however, I think they care less about your score as long as you didn't bomb it (i.e. >230).

This is a huge reason why you want to pick your aways carefully. Your Step 1 score might get you screened out as a non-rotator at some of the top-tier programs, but a strong rotation could be your ticket into them. That said, you need to play your cards correctly. I would advise against rotating at all top-tier programs, since these same programs will have rotators with great scores, grades, research, and letters from their home program.