^^^^^^^^^^^^^^I use a food processor and water with ice in a cup .
I do 2 1/2 pound batches .
I do one grind through the 1/8 inch plate .
Then I mix in my seasonings and any water it needs , and hand mix .
Then I split that in two and go in the food processor .
I pulse the blade , and add water a little at a time .
I don't add ice to the mix , I only use it to cool the water .
The half on the left is ready , the half on the right is about halfway there .
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Both halves done , and mixed together .
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Stuffed and poached . This has no cure .
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I don't get hung up on the temp of the meat paste . Process small batches and get it done .
Leave what you're not working with in the fridge . You'll be fine .
Don't over do it , or add to much water . I don't watch a lot of those videos , but I see he runs the food processor full on instead of pulsing . I think full on works the meat paste to much .
Just my opinion .
If your option is to use the stand mixer , don't add ice , use cold water .
Only add the water it needs . If it's not fully emulsified that's OK .
I believe your processing the meat too cold or in semi frozen condition. Its ok for the meat to raise in temperature. The cure will keep it safe.
some info for you about your 2 speed stuffer
2 speed vertical stuffers
I would like to clarify hand crank vertical stuffers called two speed stuffers They are not used to stuff at two different speeds, A stuffer that has two speeds are designed to stuff at a low speed setting only. A ratio is changed when the handle is moved from one spline shaft to another. When...

I don't recommend emulsifying in kitchen aid grinder or adding water to the meat while grinding. That is where your whole issue may lie.
My 2 cent
Boykjo