Hi GW:
Thanks for your post. I am also not a professional, but I do have some thoughts, although I have no way of judging if they are plausible.
Kepler finds planets by the very slight dimming of the brightness of a star during the transit of a planet. The area of a view of our moon's disk is about 7.4% of the area of the Earth's disk. If the distant planet and the planet's moon were aligned during a transit, then the reduction in the star's brightness would be about 7% less than when there was no alignment. What improvement in a Kepler-like instrument would be able to detect this? I understand that such an alignment would occur only about 0.6% of the transits. It there were one transit a year, it would take about 150 years of observation to detect one alignment.
If it were possible to actually photograph an image of the distant star during a transit with sufficient detail to make out a moon's darkness together with the planet's, fewer transit observations might be sufficient to confirm a moon was present. Perhaps a PF participant might suggest plausible improvements in telescopes that would be sufficient to do this?
Regards,
Buzz