Don't do it twice. I gave up on screens because I could not predict when I would get "screen marks" or embossing on the print. It did not matter if they were emulsion up or down. I had no problems for a long time, and then problems which I could not troubleshoot. Now I hang the prints back to back from a line with no problems and better initial flatness.
I have never tried this because I was worried that they would get stuck together. Does this not happen?