Good job there.
Although I think you would get a better result scheduling your reps, rather than going "all out".
Like do 15 in the first minute, should take about 30 seconds, then take 30 seconds rest and do 15 in the 2nd minute, then about 30 seconds rest again, etc.
So start at every minute for 15 reps, that will get you 60 in about 3 1/2 minutes.
Then just do 10 every minute after that, or whatever you can handle.
This should get your time down to 7 1/2 minutes.