Is somebody having you on?
Either I don't understand the problem, or it's impossible.
A single flip-flop only has two states; on or off. The problem you're tackling requires at least three states. You need at least two flip-flops.
If you're allowed to use two flip-flops, you might consider...
As far as pullups/downs, the pins are generally driven by discrete logic which has no floating state.
(In a few cases they are connected to configurable logic devices which take some time to 'wake up' and drive their pins. We have already identified the need to put pull resistors on these guys...
Thanks for your thoughts...
The problem is not one of maximum cycles; the data is written very rarely - nominally, only when the product is produced, and perhaps another time or two if the product is ever serviced.
The data is read more often; perhaps a few times a day, maybe as many as a few...
We have been using 93C46 serial EEPROMs (usually from Microchip, but also TI/Fairchild, Atmel, others) in our products for a number of years to maintain instrument-specific data such as serial numbers.
In the last few years we are experiencing an increasing trickle of field failures of these...