I think you are choosing the best way. Hand sewing the back is nor that difficult. Just try to concentrate and taking your time on the corners. Make sure that everything is aligned properly before you start sewing the corner in place. Here is a MSQC video on how I do it.
https://www.youtube.com/watch?v=0vCWpxBRs20
I just make a small clip because I am always worried about cutting off the strip if I had made a mistake.

These are my favorites too. Wonderful explanations and tutorials.

I use Jenny Doan's method; her tute on MSQC.

Basic simple instructions (that are reliable) are available on both the Missouri Star Quilt Company and Eleanor Burns' Quilt in a Day. If you do not want to hand sew the finish, you can attach the folded 2 1/4" or 2 1/2" strip to the back, wrap it around to the front and stitch it down on the front. (I can hear the purists screaming at me now!!!!) If you are not comfortable with your straight stitching, use a blanket stitch, edge stitch or zig zag along the binding. When I make a child's quilt, I like to do this to make sure it is secure and can be abused. I will use a decorative stitch and sometimes in an accent thread color. Bottom line, is whatever you feel comfortable doing to get it done is perfectly acceptable.

I cut my binding strips 2 1/4" wide, stitch ends together at an angle, then press in half with wrong sides together. I always lay my binding out around the edges of the quilt before sewing to be sure a binding join seam does not hit on a corner---if it does I adjust where my binding starts on the side of the quilt. Then I sew the binding on the front, and hand stitch down on the back. I do bindings in the evening while watching TV.

Grab some ugly fabric, make a small sandwich and try a couple of different videos and see what "clicks" with you. Even if you have to make a couple of sandwiches. Then, you are not so invested with doing a "whole" quilt, if you make a mistake on a practice sandwich, no big deal, just go forward to the next corner. I have found that when joining, make a 45 degree angle at one end, sew onto the quilt, when you get to the end, make another 45 degree point and slide the second point into the first point, finish.

Doing test runs on scrap sandwiches is definitely worth the time and effort.