I still don't see where the difficulty is. You need a memory registry only if you need random access to said memory, but the TM does not need it.
Sure, if you want to emulate a TM on a system that already uses random access memories, like most modern systems do, than of course you need a sufficiently long pointer for a sufficiently wide memory. But that is an accident of how systems work today, not an inherent complexity: you could easily emulate the TM in an old mainframe with a magnetic tape without ever seeing a memory pointer.