First, beat the special mission you want to go freeplay on, anyway you want. From my knowledge any special mission works.
Then, don't collect your reward just yet - Close the app, and double tap the home button on IOS, or that tab button on Android. Re-open the game and it'll start where you left off, but at the next round. Remember - the same rules follow there.
For example = No Escape still leaks lives if you leave the bloons on screen for too long.
It's not really harmful to save data, so it doesn't hurt to leave it around.