I'm okay with the set up but I'm not really ok with "random conditioning." The conditioning work needs to be planned around your strength work, and whatever you are doing for conditioning should take into account the next days strength workout.
Ex- if you do a bunch of KB swings the day before deadlifts you are an idiot. If you do a bunch of thrusters the day before squats you are an idiot. etc, etc.
I'd also consider training 2 days on and 1 day off on this schedule. More frequent off days will reduce likelihood of overtraining. What about something like this:
Day 1: Squat/Deadlift
Day 2: Press + Conditioning
Day 3: Off
Day 4: Squat/Clean
Day 5: Press + Conditioning
Day 6: Off
Day 7: Repeat
I actually have given this one out alot with great feedback. I like this one even better.
Day 1: Strength (pick 2-3 lifts and crush it)
Day 2: Conditioning - push to near death. Prowler or sprints at the track
Day 3: Off
Day 4: Repeat
Doesn't get much simpler than that.