FYI the next 9 full moons with % illumination, together with ecliptic latitude. So RET says that 100% illumination is infrequent (but not impossible).
But this will not satisfy Tom, because it is based on an RE model.
Date Illuminated Ecliptic lat
27-Jul-18 100% -0 16
26-Aug-18 99.9% -2 42
25-Sep-18 99.8% -4 47
24-Oct-18 99.7% -5 53
23-Nov-18 99.8% -4 52
22-Dec-18 99.9% -3 18
21-Jan-19 100.0% -0 22
19-Feb-19 100.0% 2 07
21-Mar-19 99.9% 3 54