I think you are slightly off... You do one samson stretch per side. Holding for about 30 seconds each side. Then fly through your 15 reps of squats, situps, back extensions, pullups and dips. Then repeat two more times starting with a 30 second samson stretch on each side.
The stretch basically acts as a minute rest between rounds except instead of just sitting on your butt or drinking water, you do a nice deep stretch.
If done at a brisk pace it should easily take you under 15 minutes. In any event, you should probably stop wherever you are after about 15 minutes. Take a 3-5 minute water break and then begin your regularly scheduled workout.
Note that on days when the WOD calls for a lot of something that's already in the warmup, like pull ups. Feel free to substitute another exercise so you don't fry your arms/hands before the WOD. Also feel free to substitute skills exercises in the warmup. Example, OH squats are great if you are going to work snatches that day, but consider subbing front squats if you are working cleans. Consider subbing lunges if you are going to work on Jerks in the WOD.
Also if you workout in a gym, have a back up exercise in case a station is being used. Since you are trying to go fast and stay warm, if someone is at the pullup/dip station, do body rows hanging from a racked bar and pushups. There is one back extension aparatus at my gym that is often in use, so I'll just do head and leg lifts (supermans) lying on my belly, or wrestler bridges. Be flexible and work fast.