Many people who don't know me well will tell me that I have a "weird way of wording things". I use a very similar strategy, and often have to reshape my sentences midway through them to work around my stutter. When I was younger, I would have to add a lot of "uh" and "uhm" to my sentences to power through them, but later on I learned to just replace words and phrases on the fly. Everyone has to find whatever works best for them. Not everyone's stutter is the same. :)