Waterbutts: I did exactly the same thing a month or so ago when I installed new butt for the front of the house. It started to overflow even though I followed the instructions nd measured very carefully.
Eventually worked out I had probably measured a little too closely (to maximise the volume of water collected before the diverter sent the excess down the drainpipe) and also not allowed for really heavy rainfall.
I bit the bullet and just cut another centimetre off the lower section of the downpipe and reattached the diverter. Amazed myself how quick it was to do.
Assuming your diverter has the the same type of design, the only thing to watch for is to make sure the upper section of downpipe is still long enough to reconnect to the guttering because that is the bit that will drop a centimeter lower when you reconnect the diverter (attached to its bottom end) to the lower section of pipe that goes into the drain/ground.