I was recently bronze 1, and did my promos for silver 5, so disregard this if you don't want advice from a silver player, but this is what I did when I got into my promotion series.
First of all, I took a nice hour long break before anything just to cool off, then do a normal round. Then I just did it. I didn't worry about the outcome of it, I wouldn't get anywhere prolonging the series and contemplating when I should do it, I just went at it, with my best champion, and with the best of my abilities.
There's nothing you can do that you already do gameplay-wise, but you can change what you thing psychologically, and doing that will help you a lot.