John, can you jack up reference pin with a diode instead ?
This will give you an o/p V of 5V+diode and allow you to use
a 9V battery as the i/p limit has also been raised by a diode V

This is something I do with zeners (k to pin, a to 0V) or trimpot
to raise o/p to non-standard voltages. With a zener you need to
have a couple of mA back from the o/p to the cathode to stabilise
it, but I "think" you can insert a signal diode (eg 1N4148) in the
reference pin path to ground, with cathode to 0V and anode to
pin without needing any feedback as above. This would give you
an o/p voltage of ~ 5.6V and an i/p range up to 9.6V

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