rdebolt - I don't think they want you to pull the controller apart at the electronic component level, just it's connection with the string...somewhat similar to putting an extension cord in the wall socket, then pulling it out until the lamp starts to dim and flicker. Basically you're creating a high resistance connection with the thought that any node 'on the edge' of failing will not be able to respond and be set apart from the others.
As for my brief foray into troubleshooting: If the whole string is doing something crazy, I'd suspect the very first node. If you're getting rainbows at different locations, I'd note the point each rainbow starts over several color intervals. Eventually you'll find a node which is the first bad actor (ie the node closest to the start of the string which doesn't make all the color changes). Most likely it's the node just before that causing troubles.
On two of my bad strings, bending/flexing the suspect nodes revealed erratic operation. You wouldn't think much would shift under that epoxy, but flexing was just enough to cause an issue...maybe a bad solder joint? On at least one node, I can visually see the corner of the 1804 chip is cracked away. The piece isn't in the epoxy, so must have happened during production. But I suspect that leg of the chip may be faulty or not firmly soldered.
If you put a few drops of baby oil or vegetable oil on the node, you can get a pretty clear look inside and may be able to visually spot an issue. This isn't too practical with the whole string, but if you can narrow it down to a few nodes, it might help spot visual troubles before cutting.