As far as only having one FTO on your CV is concerned, I can't see why that is important. I used 9 different training organisations / flying schools but it might be easier if you used the one. They probably won't really care anyway, and they will care even less where you did your hour building.
Ian Cheese's stance on this was basically consistency - as a business if you were doing a large project, you wouldn't pick and choose your providers yourself, but rather get a professional project manager who has knowledge of the area to do it. Likewise with your training, he wasn't keen on the whole "plan your own training" approach as you can't be an expert in assessing your own training. Much better to stick with one provider who can then focus on your weaknesses and improve those etc., rather than at each new provider having to be re-assessed and covering old ground and/or missing things that you need to concentrate on.
He stated that if you'd done CPL, ME/IR etc at more than 2 different providers then he wouldn't look at you. Whether this is right or wrong doesn't matter I guess, that's how it is - there are obviously enough candidates available who have used one (or perhaps 2) FTOs.