Help with Josie punk beat

Josie

I am trying to play Josie by blink-182 and am able to do it at 120bpm, but this beat should be played at 200bpm. I've been trying to slowly increase the speed but am stuck between 120-135bpm for awhile now. I can play all the parts individually at 200bpm, but putting it all together I lose all sense of the pattern and coordination at anything over 135. I am looking for tips on how to hear it or feel it or think about it differently as I keep trying to increase the speed.