I think I finally figured this out. Even though the "Start Time" selector on the Video Effect shows numbers to 3 decimal places in precison, it is in fact rounding the "Start Time" DOWN to nearest whole second. I generted a 24fps mp4 video with burned in timecode to demonstrate. Files attached.
This being the case, maybe it should have been posted under Bugs rather than enhancements, but I would still also like to be able to type a number into that field rather than trying to use the slider and not get a number that I want.