Not a bad idea. Should help. You could also look and see what your doing that may be interfering with your time. E.g. Whats your distance from where you do pullups pushups and squats. Walking more than a few feet is counter productive to your time. You could also review your technique. Are the pullups proper and kipping correctly, same format for the other two exercises. Can you speed up the rate or turnover that you are doing? I like to pump out 5 pullups hop off the bar, shake my arms out, 5 pullups etc.
Crossfit has a workout designed to improve your speed a bit on this type of workout. Essentially the goal is to get to "Cindy" or our L8D1 workout done backwards. The idea being to get comfortable doing the reps and be able to do 15 rounds within 20 minutes comfortably and then speed up/move up. So you would start L1D1 and if you complete 15 rounds with correct form go to L2D1. Everytime you find that you are messing up form you go back to square one. The trick is knowing where you are messing up the particular exercise. For me I know it breaks down pretty quickly when I fatigue. Pretty sure if I did it religiously I keep going back to Lvl 1 for a while.
"Permanence, perseverance and persistence in spite of all obstacles, discouragement, and impossibilities: It is this, that in all things distinguishes the strong soul from the weak”