I saw that the combobox has several properties for events under all properties. I tried adding
#{compositeData.onchange} to the onchange event, and it works. One caveat is that it seems to fire three times, but I can live with that.
To implement:
Add custom properties to the custom control for the events you want to have custom event handlers for. In the source code of the field, add attributes for the events you want code to run. E.g. onchange="#{compositeData.onchange}"
In the XPage under custom properties for the custom control, write the SSJS you want to run for your events.
That's about it.
I have only tested this with ComboBoxes, but I'm not surprised if it works for most fields that have event properties.
Tested on server running Domino 8.5.2 FP2