That's the first time I'd heard of having a screen "sandwich". I have three Rolleiflex ("standard" 2.8 Planar, Wide and Tele). I replaced the screens in mine with ones made by Bill Maxwell. They are reputedly the best but some people are very happy with Beattie screens. Bill can provide plain screens, screens with or without grid lines and screens with a central focus 'spot'. They are made as one piece and I've found them very good, but they are not inexpensive. The one I bought a month back was $193. Worth it in my view.
Quoting Bill:
" I make two HI-LUX screens for both the interchangeable hood Rollei TLRs (such as your Rolleiflex 2.8E2) as well as the earlier non-interchangeable hood Rollei TLRs. The screens for the interchangeable hood Rollei TLRs are user interchangeable and do not require any tools or adjustment (presuming that the camera is currently focusing ok with the original factory screen). The screens for the non-interchangeable hood Rollei TLRs can be supplied either for installation by you or a technician. The self-install kit with materials and instructions is intended for people of average mechanical ability.
These screens are:
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> (1) HI-LUX Brilliant Matte - very bright, contrasty, high clarity, all matte screen
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> (2) HI-LUX Micro/Split RF (Type II) - 4 mm diameter horizontal split image rangefinder in the center, surrounded by a 7 mm diameter microprism collar, surrounded by a bright matte field
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> All the above screens are available (a) without lines, (b) with vertical and horizontal crop lines for rectangular pictures, or (c) with grid lines. All of my products are made to order. Please allow us time to produce your screens. "
Unquote:
Bill doesn't maintain a website but you can reach him at Maxwell Precision Optics <maxwellprecisionoptics@yahoo.com> and if you're in the USA his phone is 1+770-939-6644 and you'll find him very helpful.