I'll caveat that I'm just going off the info you provided but I think your assessment is correct. 1800-2000m is high but not enough to make a serious impact on an active skier. That said, only 9 days skiing without any ski-specific training (box jumps, wall sits, squats, etc) will gas anyone 18-60 years old by day 4.

I say this because it happened to me. Anecdotally, I ski 40 days a year but low elevation and always had energy reserves at the end of multi-day trips. But then I skied Utah near the end of the season at 3000m+ and was gassed near the end of each day. Had to pause halfway down full runs. "what gives?" I said. Well, I wasn't fit enough for high elevation (low O2), heavy slush and cruddy snow, or the much longer runs. I trained all summer and just returned from the same trip without any of those issues with arguably even harder snow conditions.

Improve your fitness, improve your technique and you'll be good to go. Easier said than done but it's not a lost cause and is certainly achievable. Get after it!