Nancy, many people don't convert well, and you don't have a functioning thyroid so that would mean all your FT3 would have to come from conversion. Many cells in your body need direct T3, not the converted stuff. There's also the issue of the other Ts - altsupporthyroid has some info on this, I'm sure you've read it - research is pointing to the fact that T2 in particular is necessary for optimal health.
Face it, our own thyroids make T1, T2, T3, and T4, therefore we need them for something. This is why so many people do so much better on natural desiccated thyroid like Armour or Naturthryoid.
Anything that happens in the liver will compromise conversion of T4 to T3; alcohol consumption, ketosis, use of NSAIDs and a few medications.
Low FT3 can also be a symptom of stress - be it physical or mental in nature. Dieting for extended periods of time can raise cortisol and lower FT3 (in particular LC dieting, where cortisol can rise very high because carbs are what help control it).
You definitely need some T3 in there; I'd try the suggestion of faxing those numbers to your doctor and seeing what he/she says about them. Most doctors will say "you only need T4 because your body will convert it to T3 as needed" but when faced with the reality of a particular situation they might see the error in that way of thinking and decide to be magnanimous - it can happen
BTW, these results reinforce my suggestion that you get yourself some selenium and Vit D pronto - they'll help you make more T3 out of that T4.
For switching from T4 to a natural hormone have a look here:
Switching Hormones (synthetic to natural) and
How to switch from synthetic to natural
Nat