My first pro fitting (Retul) was on my Defy, almost two years ago. When I took it in, it had platform pedals and the fitter asked if I was going to exchange them for clipless before the fitting. I did not want to go clipless or use toe clips because I was extremely uncomfortable with the idea of being connected to the bike and not being able to take my feet off the pedals in a hurry. He told me that he would do the fitting, if I still wanted to, but I would not get the results that I would expect for that type of fitting using my existing pedals. Not to get into a clipless vs non-clipless discussion, but I decided to change to clipless pedals before the fitting and I am so glad I did.

Before you decide, if you haven't already done so, I would go and talk to each of the fitters (BG and Retul) and ask them this same question. Let them explain the whys and why nots and then decide which fit will be best suited for you. And as bigfred posted, " there's no reason why a "good" standard, professional fit shouldn't be able to address any back or knee issues that can be addressed through the fitting process."