The place on the back, where little tucks happen during the quilting process are called kisses, so they serve a purpose? <g>
I am not sure how you are working with your quilt in the sewing machine, but I have done fancy machine quilting on a portable sewing machine, and my sister in law, using a walking foot, does queen sized quilts, stitch in the ditch - quite handily with her sewing machine.
No quilting machine and frame? No problem .. quilters have been doing it this way for DECADES! so, <g> you will be fine.
One of the things I do is roll the edges of the quilt that is on the inside of the quilt, work from the middle out, what is in the throat area gets smaller.
I was watching Simply QUilts one day, and the lady that did machine quilting on her portable much better than I have ever gotten, said ... keep it fluffed up ... she didn't necessarily fold it or roll it, nor, did she have the quilt laid out flat and neatly ... she just made sure that the quilt was as loosely laid out as possible, so that the weight of the quilt was not dragging on the machine.
Following her lead, I keep the quilt sort of laying in my lap, over my shoulder, I lift it often to make sure that some fold hasn't gotten caught under the table, or in the leaves of the table ... and breathe!
I make sure that my sewing table is as close to a wall as possible so that the quilt can't escape away from me on the other side of my sewing machine. And, if I have to, I bring an ironing board off to my left side to help me support the quilt. The ironing board is cool because it can be level with whichever table I am using.
You will be fine ... <g> the secret to having few kisses on the back is to make sure you have pin basted enough (four to six inches) as others have mentioned. Let us know how it worked out for you, and any tips you picked up to succeed at your quilting!