Okay, I've found a couple places that have images of machines that look like they might take this monogram attachment. One of them is this site with instruction manuals for sale
. They offer images of the machines for comparison with your own.
The machines that seem likely to be compatible with the monogram bobbin plate are all 158 machines with these sub-model categories:
1400, 1410, 1430, (1431?), 1503, 1504, 1515, 1601, 1602, 1603, 1650, 1652, 1653, 1654.
Other models have different bobbin arragements and architecture that look incompatible with this monogramming bobbin plate. Most of the images for these machines look like they don't use the super high shank presser feet. So if one of these models is super high shank, that's probably the one for which the green tray box was made.
The monogram cams are identical to those made by Singer for various Singer machines. At one point, it looks like Singer made cams for Kenmore-branded machines. The same cams are used in different machine attachment systems.
I'll probably keep the trays together as a set. Perhaps one day I'll own one of these other Kenmores.
I still wonder whether there is a monogram attachment for this machine. It would make sense that it would use the same pinion that sits under the pinion cover plate of my 17851.
I'd be grateful for any insights others may have on this model and the likelihood of a monogram attachment for it.