Hi Rachel, as you may have guessed from my previous post I hate running and if i never ran again i'd hardly shed a tear.
Having said that though running can be important for certain applications and it sounds like you fit into that category.
Although your SAR team THINKS that endurance is king they are ignoring the fact that at the pointy end of a rescue you may need strength, speed and strength endurance to pull of the important bits.
If a bunch of marathon runners tried to rescue me and some of my friends they'd be up the creek because none of us are feather light. Me, I can carry a marathon runner under each arm! (ok slight exaggeration)
If you have the fitness to run 5km in 25-30 min then you can probably walk for long distances just fine however i'd be inclined to do some tougher runs with 10-15kg of gear on.