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It's running on the MBP now. Apparently the F-Secure anti-virus software running on the machine doesn't like Sage and blocks it's execution (even though it doesn't say so in its logs). Removing the previous 10.12.3 installation and reinstalling if from scratch with F-Secure disabled solved the issue. Anyway, the next thing to resolve is how to automatically start the jupyter interface rather than the old notebook, but I guess that's another thread...

BTW, the iMac had the same issue. It starts the app now, but unfortunately doesn't like the 10.12.3 dmg. When starting the app, it opens two terminal windows, one of which shows the error messages copied below. I'll try the 10.11.6 dmg later.

10.12.3 dmg error message on a late 2012 iMac:

iMac-of-Tony:~ tony$ '/Applications/SageMath-7.6.app/Contents/Resources/sage/sage' --notebook=sagenb
Fatal Python error: Py_Initialize: unable to load the file system codec
  File "/Applications/SageMath-7.6.app/Contents/Resources/sage/local/lib/python/encodings/__init__.py", line 123
    raise CodecRegistryError,\
                            ^
SyntaxError: invalid syntax

Current thread 0x00007ffff04043c0 (most recent call first):
/Applications/SageMath-7.6.app/Contents/Resources/sage/sage: line 130: 11912 Abort trap: 6           "$SAGE_ROOT/relocate-once.py"
Traceback (most recent call last):
  File "/Applications/SageMath-7.6.app/Contents/Resources/sage/src/bin/sage-notebook", line 7, in <module>
    import argparse
  File "/Applications/SageMath-7.6.app/Contents/Resources/sage/local/lib/python/argparse.py", line 85, in <module>
    import collections as _collections
  File "/Applications/SageMath-7.6.app/Contents/Resources/sage/local/lib/python/collections.py", line 21, in <module>
    from operator import itemgetter as _itemgetter, eq as _eq
ImportError: dlopen(/Applications/SageMath-7.6.app/Contents/Resources/sage/local/lib/python2.7/lib-dynload/operator.so, 2): Symbol not found: __PyUnicodeUCS4_AsDefaultEncodedString
  Referenced from: /Applications/SageMath-7.6.app/Contents/Resources/sage/local/lib/python2.7/lib-dynload/operator.so
  Expected in: flat namespace
 in /Applications/SageMath-7.6.app/Contents/Resources/sage/local/lib/python2.7/lib-dynload/operator.so
iMac-of-Tony:~ tony$