Some words of caution are required here. I discussed your question with a good friend of mine and a very qualified professional electrical design engineer (PE) with decades of design experience in the wire and cable industry. This is what he had to say:
"The shorted screens would only be a problem if the drain wires were connected to individual grounds where there was a significant ground rise potential between them. Assuming the pairs are all terminated locally, then this should not be an issue. Also, I believe that drain wires are usually grounded on one end only."
Ground looping could indeed be problem and therefore I recommend you tape each shielded pair with a third and final overall polyester tape to prevent shorting and possible ground looping. Remember, you have no idea how the cable will ultimately be used
Another way is to purchase the composite tape with the polyester width extended on both sides beyond the aluminum width. Thus, when it is helically taped for 100% shielding, the polyester component would always prevent shorting.
Sincerely,
Peter J. Stewart-Hay
Principal
Stewart-Hay Associates
www.Stewart-Hay.com