SN75LVDS83B: Radiated emissions problem

We use SN75LVDS83B to transmit video from an Am335x processor to an LCD display.  We fail emissions testing when LCD video is enabled in the Am335x, we disable the video and we pass.  Removing the LCD and cable did not solve the problem.  Putting the SN75LVDS83B in shutdown did not solve the problem.  Removing a series resistor on the LCD clock line between the Am335x and the SN75LVDS83B solved the problem.  The layout does not follow TI's recommendations.  It has one solid power plane, only five bypass capacitors for the whole chip that are all 0.1 uF and not placed and routed well.  Are the emissions problem likely related to not splitting power planes and not following bypass recommendations, or should I be looking for something else before the company spins the board?  The LCD clock is approximately 33 MHz (dithered) and emissions are most problematic in the 960 MHz - 1000 MHz range.