What is the texture of the sausage like when you're eating?
I have the same mincer and mince once on the coarse plate, mix, then stuff using a dedicated trespade sausage stuffer.
I then leave the sausage to hang/mature overnight which also helps them swell a little.
Sticking the head of the mincer in the freezer helps, but making sausages using the mincer is difficult and the texture for me never came out right.
Which is why I bought the stuffer.
I also only mix venison with beef for a much better sausage.