I do a total mix up of it all. Competitive kids train several days a week, if you run it the same way everyday they will become tired of it and thats when you will have the cheating.
Do all the things you mentioned and more. Keep it fresh.
You can also reduce the rushing if the kids understand the purpose of each drill. They get a lot more excited about doing it when they can see where its leading. Explain why a certain drill has to be faster or slower.
But the biggest thing is keep it fun. Kids love to condition when you throw in little unexpected things. Instead of just doing V ups have them do V ups on a crash mat so its squishy or a small box so they have to balance, do arch holds and front supports between boxes. Don't just handstand walk up and down the flow set up an obstacle course which they have to walk around. Don't just do handstand holds have them try to do it on a variety of different (but safe surfaces). Don't just do candlestick to straight jumps or burpee's to straight jumps have them try all different kinds of jumps after it - tucks, straddle, pike, wolf, ring, sheep, double turn - whatever you can come up with (that is safe). Don't just to chin ups - have them do a set number with their partner on the other side of the bar then they have to monkey across and change places and chin up on the other side without falling off. Make your conditioning into games, competitions and challenges. These are just a few ideas the possibilities are endless.
Have weird equipment set up for your drills and conditioning. Nothing sparks the kids interest like bring lots of bits of equipment over to make a drill, they get so excited to see what they are going to do. And even if its usually something they find hard and boring they are begging to have one more turn of it.