Ey I do a ton on hair straightener pressing (lol what a bragger!)
To me its def strain specific but also high temps and long presses can make a more runny oily product. If u can get the temps lower and do less time pressing. And then repress those "pucks" again a little later, at a higher temp.
Thats what i do. A hair starightener is too crude to dial in precisely, but i can adjust my "tech" some to compromise.
Just a thought, i hate hving those runny papers! U can also get some tacky rosin and use it to dab up the runny stuff, but i bet u will need to be inside your freezer door to collect

I never tried the clamp style so i am not sure how quick a press can be.