Let me explain, shortly, why I believe a mountain defence by fixed defences to be both effective and not necessary right now.
Basically, you can classify mountaineous terrain in three different types: Passes, human-traversable and steep faces, in reversed order of ease of defensibility.
Steep faces are difficult, but possible, to climb. They necessitate, however, taking only a few things with you. This is pretty impractical for sustained military operations and can therefore only be used to facilitate attacks on the other two types. Patrols are the easiest way to check them - it should be pretty easy to shoot someone who's climbing and doesn't shoot back.
Human-traversable terrain looks like a hill or so, that is a fairly steep incline and maybe a few parts where you've got to use your hands. They're easier to traverse, possibly with mules, but you can't take heavy gear with you. Here, a few heftier firefights might break out, but again, if they climb down they'll be crushed (due to no supplies), if they don't, they have no supplies.
Now, passes. They are the least common territory, and facilitate the transport of heavy gear. Railways go through there, just as roads. Such a road (and railroad) is usually a serpentine, with mountain to one side and an abyss on the other. Here, fixed defences will be necessary and practical. A single machine gun bunker should be able to suppress hundreds of enemies, as they probably lack cover (you need a second however to cover reloading and barrel changing). And, you need to secure the bunkers against nearby enemies infiltrated via one of the other ways.
There is one problem with this, though: The country across the mountains is neutral. I believe we have a more pressing concern to address.
On a side note, anyone knows a good diceroller that can roll large groups of dice at once. The wizard of the coast one seems broken. It has a tendency to give streaks. Ie, either lot's of flaws, or lot's of succeses.
If you want to, I can write you one. Give me a bit more details (like what types of dice, how detailed you want the results), and wait a bit.