Are you guessing, James? Where did you get that info. regarding the chip? See below.
"As VCC falls below approximately 3.0V, a power switching circuit turns the internal lithium energy source on to maintain the
clock and timer data functionality. It is also required to ensure that during this time (battery-backup
mode), that the voltage present at INTA and INTB (INTB) never exceeds VBAT. During power-up, when
VCC rises above VBAT, the power-switching circuit connects external VCC and disconnects the internal
lithium energy source. Normal operation can resume after VCC exceeds 4.5V for a period of 200ms."
The above is from the datasheet for the ds1486-120, so maybe you misdirected yourself, unless I misunderstood the above?
Secondly, have you measured the current draw as the battery can be much larger than the one in the chip!
Third, could not a circuit be built to block the current to the other parts of the board with a transistor driven and triggered by the board's own 5v (tying the emitter and base of npn together) and then it would block the 3.5v from the external battery to the rest of the board when the unit is off? Of course this would mean lifting Vcc pin.
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If the details and proper component selection are worked out, this would be a heck of a lot easier than replacing the chip and further, the chips are costing more than I paid for my scope these days.
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