If the question is about complicated procedures, some have developed the concept of bloatocracy, applicable to a state, or a system in general. For instance in Bloatocracy and Ineptocracy, one can read:
In a bloatocratic system, it is beyond the capacity of the ordinary
citizen to be aware of, keep track of, and do all the laws, rules,
regulations, policies and procedures that are required of him or her.
Workers, employees, customers, and users of these businesses and
institutions find themselves increasingly frustrated and unable to
walk through the paperwork required to do even the most basic things.
So, bloatocratic could apply to the question.
However, the situation described in the OP's example is a different situation. Rules are quite simple, they just don't match. I was thinking about four options: deadlock, stalemate (from chess, aka pat or pat), impasse, and finally Mexican standoff .
For deadlock (my favorite here), I quote the concurrent computing sense, because your banking process involves e-mails and wire transfer. And in bureaucracy "it's always the fault of the computer".
[it] occurs when two competing actions wait for the other to finish,
and thus neither ever does
The above page also refers to Catch-22, and oddly, there exists a Banker's algorithm, which is:
a resource allocation and deadlock avoidance algorithm developed by
In popular usage, the word stalemate refers to:
a conflict that has reached an impasse, and in which resolution or
further action seems highly difficult or unlikely.
In chess, this is a situation in which the player who have to play "has no legal move"
The word impasse is more generic:
may also refer to any situation in which no
progress can be made.
And a final one: a Mexican standoff (or shootout),
a confrontation between two or more parties in which no participant
can proceed or retreat without being exposed to danger