In the extend statement the controller name was still 'sap.m.Timepicker' and a core function used this to generate a require statement for 'sap.m.TimePickerRenderer.js.' After changing this to our custom namespace.TimePicker.js the core function generated the correct require statement and the control will render.
However the .css is missing as well and needs to be added (we added to our custom theme's css using theme designer) as well as some Text variables have to manually set since the resource bundle doesn't contain them.
I have a doc on issue if someone sees this and needs more info.