Bill, what you are doing is almost exactly what we did in college many years ago and I continue to do today - what I do different:
I make folded "sleeves" slightly bigger than the prints (I have sets for each size) made from a roll of glassine (recommended to me for this purpose many years ago by a museum conservator - and cheap). I place each print in its own sleeve, so 2 layers of glassine between each print. Prints are face to face, back to back alternating. I try to line up all the corners, usually they are the same size. I use full size sheets and trim later if needed. This avoids crease marks from the edge of one print to the face of another.
I also don't go that high on the press, just till it is just too hot for me to hold my hand to the patten, but let it cool till room temp, and then a day, if I can wait.
I don't do more than 5 or 6 prints at a time, and they never stick to the glassine.