I think I get that - the existing door motor box has an input that is continuously monitored.
If it transitions to grounded, the door closes then the motor shuts off. If it transitions to open, the door opens then the motor shuts off. The existing timer has volt-free contacts that shorts that input to ground when the door is scheduled to be closed.
As is, even with the relay, it has to maintain its output until the timer 'catches up'. The drive current for the 4N24 is killing your power consumption. Even at only 1mA (and I suspect you are using far more,) that's equivalent to a weeks power for a PIC in sleep mode, worst case, and probably something like 6 weeks to 2 months power if the typical figures are to be believed.
Interfacing to the door motor without extra quiescent current isn't a problem - a N-MOSFET can do that easily. The problem is the timer output - its grounded for the entire door closed period, so if you simply use a pullup resistor it will be drawing current whenever the door is closed. You can mitigate that by using a high value pullup, but that increases the sensitivity to noise, and although you can use a debouncing algorithm to ignore the noise, the increased average current consumption due to unwanted wakeups during the door open period could be worse than the pullup resistor consumption during door closed.
If the pullup is under about 400K you'd do better to enable the watchdog timer (using SWDTEN), and use it to provide a wakeup every minute or two, during which you enable the pullup (by setting an output pin driving the other end of the pullup to '1'), poll the IN signal and then turn the pullup off (actually turn it into a pulldown, by setting its control pin to '0'), all within a few ms.