I think youve got a couple of options.
Firstly if you are planning on the more XC routes your SC will be fine once it's "Beefed" up with a short stem, wide bars and big tyres. Personally I would also try and get a hold of a second cheap wheelset as it is notoriously rough on equipment and it would be shame to spoil what you've got.
With the money you've saved you can hire a DH bike for a day or two. I hired a proto DH with BOS front and rear for 70euros for the real big/steep/techy stuff.
The other option is buy something cheap(£1000 approx) and sell it when you get back. The alps are notoriously hard on equip so in some ways it makes sense to save your pride and joy. If you go down this route I wouldn't bother with a pure DH bike unless you don't want to go exploring and stick very local. The best trails tend to be further afield and require linking up lifts and traversing sometimes varied terain so I would say something about 7" front and rear, ideally single crown with a double and bash. A single crown helps with the switchbacks, a double will let you climb too.
The advantage of this setup is that those unmarked trails you find and explore are less likely to throw up any really nasty surprises.
I would also suggest at least one uplift weekend with your chosen setup before you go.
Finally make sure you've got the biggest, most reliable brakes, because of the sheer steep angle of some of the trails mean you have to brake ALOT. Don't scrimp here, you will regret it when you have either crashed due to the dreaded "lever to the bar,no brakes" moment, or are watching your mates fly by while you wait for yours to cool.