Also I've heard that some places in Patagonia can be really commercial and touristy. i want to avoid this kind of thing if possible.

It seems most people go there in summer; December through March so I would guess you would miss most of the crowds at the time of year you are going.

Although I've been to South America several times (but not Patagonia yet), I wouldn't have the slightest idea where to find a job (I go there to get away from my job ).

Anyway, May through August is the typical time to climb in places like Peru or Bolivia, but those areas aren't really ski touring destinations (though people do ski at places like Copa, Hualcan and Mururata). June through August is also good for much of Ecuador, but it really isn't a ski touring destination either (though people do ski some of the volcanoes). Colombia and Venezuela are usually plagued by bad weather at that time and it's not the best time to go. Northern Chile and Argentina are desert so finding good ski conditions would be chancy.

Because of all of the above, the Lake District (or Patagonia) seems like the most logical choice, though I wouldn't know where to find a job. It seems that somewhere like Bariloche would be as good as any, but of course it's touristy.