+1 for treating Queue.put() specifically as the case to be handled, as that's the mechanism that can be used to *avoid* running complex operations directly in __del__ methods and weakref callbacks.

For testing purposes, the current deadlock can be reliably reproduced with sys.settrace:

```
>>> import sys
>>> import queue
>>> the_queue=queue.Queue()
>>> counter = 0
>>> def bad_trace(*args):
...     global counter
...     counter += 1
...     print(counter)
...     the_queue.put(counter)
...     return bad_trace
... 
>>> sys.settrace(bad_trace)
>>> the_queue.put(None)
1
2
3
4
5
6
7
[and here we have a deadlock]
```