You need to reset the counter whenever you change the period. What can go wrong is, if you shorten the period, the counter might have already gone past the new period value, and then it won't trigger the interrupt until it has counted all the way to 0xFFFFFFFF, wrapped around to 0 and got to the new period value - which is why it takes a while to speed up.
The line REG_TC0_CCR0=0b101; restarts the counter. You need to put it just after REG_TC0_RC0 = incomingValue*1000000;