Does the supply current vary during read depending on the stored data?
If so, you *MAY* be able to retrieve bit 6.

It is a little difficult to be certain when you don't know what it
should be, but if you stick a sense resistor in the VCC supply (maybe
with two diodes across it to prevent excessive drop while switching) and
scope that and the read signal while reading the chip, you may find you
can tell the difference when the lower MOSFET in the D6 output stage
switches on to attempt to output logic 0.

If so, a PNP transistor, a few resistors and an inverter (possibly with
a tristate output controlled by the read signal) may be enough to build
a 'gimmick' jig to let your programmer read it.

I can try that, interesting thought, thanks.