A couple of things: Have you ever tried just grounding the center tap of your heater winding? If you did, what were the results?
Second, I presume your Voltage divider is across an already-filtered supply, correct? So, I would use a smaller cap as bypass in order to use something other than an electrolytic. Of course, that generally sets the practical limit to less than 1 uF, but I don't think you are necessarily looking to filter out anymore ripple with the bypass.
Oh, I guess I have one other question: What are you using for heater wiring?