I wear an elbow brace and a wrist brace when stropping as well as using a thumb cot. This is only because I am honing and stropping so many razors a day and for so long. Sounds like you may be tense as you are noticing or you may be using some pressure and stropping at an angle on the strop that is not a natural back and forth motion.

You really just want very light pressure and try to develop a natural rhythm as previously mentioned and the rolling on the spine to change directions should just fit into that rhythm. Too light a pressure or being tentative will also throw off your stroke and feel uncomfortable as well as probably tear up your strop.

Have fun.