I simply cannot wrap my head around the fact that a note can be split, then put back together and leave no physical evidence etc.
There is physical evidence. For example, embossing would give the game away, but the fakers are sharp enough to realize this and press all the embossing out before putting their wares on the market. There are other ways to detect the fraud but I'm a bit reluctant to explain on a public forum lest the bad guys see it and try to figure out some means to hide the evidence, though I do not imagine it could be easily accomplished.
Congratulations to Canada-banknotes who made the connection with the EGU "discovery" - excellent work!
Whole or part sheets have nothing to do with the case, other than to facilitate out of register concoctions.