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 have succesfully retrieved bit 6 with a pnp transistor, some resistors and
a inverter directly at the output pin. Then came the weird part, I had to
invert it a second time to get it right. So this problem is solved.

Thanks all who contributed!