I don't use stabilizer. Your batting and batting add enough to the fabric to hold those stitches without shifting.
To help the quilt move freely without getting caught on the corners of the table, I put my machine on the floor. The arm moves freely and the quilt moves well with it.
Measure well the center of the block for placement of the design. When you turn on the machine the foot usually goes to the center of the hoop and the design moves from there. If you mark either with a pin or a little mark where the center of the block is, you are telling the machine where you want the center of the design to be, and the machine will tell you if it can be done or if it needs to be rehooped.