Stairmasters can be tricky to use for this sort of thing as the stairs fall way under you and you are not required to raise you body weigh upward. You will also need to adjust the machine’s perception of your weight to account for the pack weight. I’m no expert on stair machines but some are not motor driven and are powered by you the climber so require more work to turn them.
Understand the problems with terrain limitations though, and aside from making a completely unhelpful and snide comment about moving to place with hills the best I can recommend is to do the ME workout(s) on a real hill on the weekend (yes they could even be back to back if/when you come to that stage). Then do the aerobic base work and maintenance on the t-mill/stairmaster mid week.
I hope this helps.