If the tool plate and ratchet have been machines accurately they it should all stay in line. You have guessed right and yes you do have to shim tools up to get on centre.

Where are you based ?

One problem with gang tooling is that the Orac doesn't have a great travel in the X axis to get different holders on.

Short term, if the bearings on this tool changer are OK and not got loads of bag in them is to replace the ratchet wheel with a wheel that has 8 ? holes in it and use a detent pin to locate it after turning by hand, like the example you linked to on YouTube.