Assuming you get the moisture content low enough and vacuum pack with oxygen absorber in Mylar I would think you could get 5-10 years or more. Might depend on whether your applesauce contains sugar or not. Natural would be best. Dried apples flushed with nitrogen in #10 cans last up to 25 years...oats 30 years...interesting experiment.
The ingredients by themselves will last a long time. The interaction and the apple chips I'm not as sure.
Hard tack isn't 'that' hard. You can break it and it crumbles fairly easily, it's more that it's chewable. Make it yourself and see, it's easy and consider they have hard tack that's 150 old in the Smithsonian, pretty sure it will outlast this.
If it lasts 7+ months with no special storage (see comments), removing the oxygen would surely increase this considerably. I wonder if you could flash freeze it and then put it back in a low temperature oven to achieve a poor man's freeze dried effect to extend the life even longer.
I think I'll stick with the traditional recipe.
Shame we can't purchase Sailor Boy Pilot Bread here... I would purchase a couple cases in a heartbeat.
I was talking to my kids the other day (they've been learning about war etc at school again lately) and we are going to try abd make hard tack but add some oats and golden syrup. Kinda like anzac biscuits but without the butter. We will vacuum pack some and put some in ziplock bags to see how long they last.