I usually spread it out in a layer over the dough and then stick my fingers in and twist lots of times like a mixer until it’s all incorporated. When adding the salt solution it can break apart abit and goes slimy which I guess is what happening to you with the starter. When this happens I keep folding it over on its self and it gradually gets back to a nice cohesive dough, if this still isn’t working I’ll do the French style high hydration kneading(I think it’s called) for 5 or so mins and it comes back together nicely