Schoolmarm

I've made nearly one hundred quilts of various sizes, quilting them all by hand. I am trying to teach myself to machine quilt. I have some charity quilts that I wanted to do and they are required to have machine quilting. My finances are too tight to consider paying someone to quilt it for me. Every time I try I get gathers on the back.
I've read on the quilting board where they suggest spray adhesive, but I cannot spray chemicals into a quilt I plan on giving to a child who already has health problems. Some hospitals where I donate quilts, request no spray adhesives.
I've tried the walking foot. I've pinned the quilt. I've rolled, I've scrunched, and I’ve nested. I've tried feed dogs up and feed dogs down.
I'm using a Necchi4825. I purchased the walking foot and the darning foot. I’ve yet to try to use the darning foot, though.
I typically lay out my backing fabric on my carpet and T-pin it down. Then add the batting and smooth it down and T-pin it on top of the backing. Then add the top and T-pin it down to the other layers and then start in the center and pin. I pin a pin in every square and the same distance apart on the border. This particular quilt is 5" Around the World" pattern made up in a 45" x 60" toddler bed size.
I tried quilting up one side of a column of squares and down the other side.
I tried to quilt around individual squares as if hand quilting. No matter what I do, I keep getting puckers on the bottom side. I’ve tried to stitch in the ditch. I have not tried the free motion quilting yet as the posts I’ve read and the tutorials I’ve watched have listed these other methods as easier. I continue to get unsightly puckers on the bottom.
I do not live where there are lessons given in machine quilting. I've watched every tutorial I can find. Does anyone have any suggestions for me?
I’ve included a photo of a similar one that I hand quilted.