A lightweight interfacing ironed to the wrong side of the top most likely won't show at all, so I wouldn't worry about making it really narrow. You would have to be very careful not to stretch the top's edge as you iron on the interfacing.
What I would do is measure the top through the middle in order to decide how long the edge should be. Cut a lightweight interfacing to that measurement (cut down the middle of the interfacing to get two edges exactly the same length). Fold the interfacing in half, then fold in half again, and mark each fold with a permanent Sharpie. Do the same with the quilt top (just keep the permanent Sharpie marks inside the seam allowance, or use a thread tack in an obvious color, or chalk or pins). This allows you to distribute any fullness in the top evenly. Pin the fusible side of the interfacing to the quilt top edge, matching registration marks. If there is a lot of fullness in any area, this is where I would hand baste with a single thread to distribute fullness evenly within the quilt top.
I would pin a length of parchment paper to the ironing board and iron the interfacing on with the wrong side of the quilt top facing up. I'd probably have the interfacing extend a little beyond the top's edge. Just peel the parchment paper off while the paper is still warm, then trim the excess interfacing away.
You can test your interfacing on a few scraps but, I think as long as you use a lightweight interfacing, it is not going to show through to the right side.