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Upon further investigation, I am no longer convinced that "reduce cycles" are necessarily fatal to pickling. I am attaching a script testcycle.py that allows creating cycles using various containers. It takes the name of container class as an argument and prints SUCCESS/FAILURE followed by annotated pickle disassembly. It turns out that self-referential tuples are pickled successfully even though being immutable, they must receive their state through arguments:
$ ./python.exe testcycle.py tuple
SUCCESS
 0: \x80 PROTO 3 Protocol version indicator.
 2: c GLOBAL '__main__ C' Push a global object (module.attr) on the stack.
 14: ) EMPTY_TUPLE Push an empty tuple.
 15: \x81 NEWOBJ Build an object instance.
 16: q BINPUT 1 Store the stack top into the memo. The stack is not popped.
 18: } EMPTY_DICT Push an empty dict.
 19: X BINUNICODE 'foo' Push a Python Unicode string object.
 27: h BINGET 1 Read an object from the memo and push it on the stack.
 29: \x85 TUPLE1 Build a one-tuple out of the topmost item on the stack.
 30: q BINPUT 4 Store the stack top into the memo. The stack is not popped.
 32: s SETITEM Add a key+value pair to an existing dict.
 33: b BUILD Finish building an object, via __setstate__ or dict update.
 34: 0 POP Discard the top stack item, shrinking the stack by one item.
 35: h BINGET 4 Read an object from the memo and push it on the stack.
 37: . STOP Stop the unpickling machine.
highest protocol among opcodes = 2
There is a comment in save_tuple() that explains how it works:
 # Subtle. d was not in memo when we entered save_tuple(), so 
 # the process of saving the tuple's elements must have saved 
 # the tuple itself: the tuple is recursive. The proper action 
 # now is to throw away everything we put on the stack, and 
 # simply GET the tuple (it's already constructed). This check 
 # could have been done in the "for element" loop instead, but 
 # recursive tuples are a rare thing. 
I wonder if the same trick could be used in save_reduce() to resolve #1062277 by pickling "reduce cycles" correctly instead of bailing out when they are encountered.