Not a very complicated problem IMO.
I was just about the say the very same thing. These days astronomers use CCD devices to capture long term exposures.
A simple program to shutter the CCD for the brief second that a sat passes by, and no streaks. The satellite flyover times are well known and predictable, so it would be a trivial exercise.
Either real-time or post-exposure processing via computer makes this problem trivial.
However, depending on the frequency and number of transits expected within the field of view ("FOV") / exposure time, it might be better to blank the CCD for the full duration of each transit of the FOV, rather than "blink" just during object occultation.
Both approaches are matters of milliseconds...
That would negate any problem with intra-telescope reflections... And would eliminate any need for post-processing.
Much ado about nothing, IMO.