You might consider the ‘tie them up by their legs method’. We use this and have great success. It’s a simple sliding knot that I loop over their feet and pull tight. I let the birds hang for a few minutes as this seems to ‘knock them out’ (mostly) from all the blood rushing to their head. Once I cut the carotid arteries the birds bleed out with minimal stress to them or me. When we are doing more than one or two birds we use a multi-stage processing setup with one person dispatching birds, another dunking them in hot water and tossing into the chicken tumbler and final plucking, and another dressing and cleaning the birds. This is our usual late Fall processing setup for a couple dozen birds and it works for us.