I found out, that a block's property 'Name' cannot be duplicated in the same subsystem. This means, that unique IDs can be given by using all the parent subsystems of a block plus it's name. As subsystems are also just blocks, this means, the parent hierarchy is duplicate free, as well.
E.g. the blocks called "Add1", "Add2" and "Clock" in the subsystems "Main/Precomputation" may be given the unique IDs "Main/Precomputation/Add1", "Main/Precomputation/Add2", "Main/Precomputation/Clock".
I did not yet find a way to clear the handle cache, but this way, I don't need to.