I don't know if you've considered this, but in mountainous regions, arable agriculture isn't the only option. A lot of agriculture in Austria involves a method called transhumance. In this style of agriculture, the flocks and herds are moved up to high pastures in the spring/summer and kept up there as long as possible. This leaves more fertile land lower down to concentrate on winter feed and food for the farmers.
My uncle uses a similar method although the altitudes aren't as extreme. The flocks and herd graze the common land on the Beacons from about April until early October and all they need is care from shepherds and an intense two weeks for shearing. This leaves the good land he has (about thirty acres) to be planted with sugar beet and some type of hay for winter bedding and silage as well as the more intensive uses like market gardening and some potatoes.
It's a fairly self-contained system and whilst it's a hard life that's dependent on the weather and a little bit of luck you can scrape a living off what is essentially rock.
My uncle's farm is about half the size of an Austrian mountain farm and he raises a flock of over five hundred mountain sheep, a hundred heritage sheep, twenty Welsh Black cattle and assorted pigs, goats and poultry that are more a hobby than an industry. The farm rarely has to buy in fodder to sustain these animals and in addition produces enough fruit, veg and potatoes to feed about fifty people as well as the family.
The only thing it doesn't produce is bread as we don't grow wheat. Switching some of the potato acres to oats would solve this.
Now, assuming that the farm would operate on a much less efficient footing without modern technology (not as inefficient as a big farm but the tech does make life easier), these farms are still viable. If we assume that the farm can sustain 20% of its production (I'd guess more like 50% but let's assume less), the farm could still sustain the family and workers (fifteen people) and twenty other people with a fairly balanced diet. If people are growing their own potatoes, the meat and milk production could sustain up to thirty more.
Bearing in mind the farm is half the size of the average Austrian Alpine farm I would guess that an Austrian farm would sustain thirty people on the land and provide food for another hundred (some sort of starchy food would need to be grown in addition to what my uncle produces).
At present there are about 70,000 such farms in Austria and they are located in areas that wouldn't necessarily be ravaged by war.
So by deciding how many of these farms survived in your version of Austria, it is feasible to support populations that are larger than the available arable land would suggest: maybe not much larger but enough to give you more confidence in being able to support the factions you are imagining. The diet would be boring: skimmed milk and potatoes as standard with a small amount of mutton or beef with the occasional egg or foul or bit of pork. The sugar beet is a big advantage as it can be processed and provide a nutritious winter feed for the animals as well as providing some sugar in the diet (probably in the form of alcohol as you'd need to be smashed regularly to endure such a boring diet).
I hope this helps and isn't too boring to read.
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