Can you slip a rope over their legs so you can dip them deeper into the water and make sure their feet go under also?
I used to help my cousins on slaughter day - chickens and ducks - and if I recall correctly, they had a short piece of wood with a rope tied around it. On the other end of the rope was a slipknot that they would put around the feet after they had bled out in the cone. This was used to lift and carry the bird through the plucking process and to the table for gutting. They would dip the birds into hot wax, they hang them to cool off a bit before pulling off the wax and feathers. They were then carried into the house where my aunt and her SIL would gut, cut off the feet for stock, sort the organs (heart, liver and gizzards) and pull the pin feathers.