Kentucky Fisherman The second grind is always going to be slower and this is doubly true when going from a 3/8th plate to a 1/8 plate. By breaking the meat down into a ground product you are making it harder for the grinder to push the meat down to the plate and knife and you are also trying to make it go through a smaller plate. Best thing i can tell you to fight this is to get your meat ICE COLD before grinding, some ice crystal forming on the meat is just about right! This will speed up the process and improve your finished product.
With it looking like bologna I have the feeling your 1/8 plate, or the knife you use with it, are in need of sharpening or replacement. What you are describing sounds like your plate and knife are smooshing your meat instead of cutting it cleanly.
As for the stuffing, yes, trying to stuff snack sticks off of a stuffer is incredibly difficult, frustrating and annoying! It is much easier to use a stuffer when making any type of sausage but especially when making snack sticks.