[bmacho]

> You're right, I misstated this - but I don't think this is fatal.

It is crucial at this types of results, when you search for a proof.

There are a lot of things true, better make a table of it, instead of a wall of text:

  - If you observe the machine halting, ZFC is inconsistent. 
  - If the machine hasn't halted yet, you don't know if ZFC is consistent or not.

  - If ZFC is inconsistent, the machine will eventually halt. (You have an upper bound for this, given a contradiction.)
  - If ZFC is consistent, then the machine won't halt ever.

Also it is consistent with ZFC that this machine halts, since it is consistent with ZFC that ZFC has a contradiction. This means that if ZFC happens to be consistent, and you work in ZFC+contradiction, then you will know that your machine will eventually halt, yet it won't halt ever.