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Place your subject close to a plain background and you will most definitely see the Speedotron BD ring.
I've done the background test...even did the OCD thing and tested it on a Munsel N8 projector wall. Yep, it's there (but w/ the Einstein, it looks more like a hotspot like what you see from the Maxilite...bright even round area w/ quick falloff to a lower light area....it's very much a ring w/ a WL). In most situations, you won't notice it. In the one you described, it's easy to work around by aiming it differently. So at least for me, not an issue...