Welcome to Flyertalk, and welcome to the BA forum RRAway, it's good to see you here, less good to see your trip being disrupted this way.

Yes, so long as you keep the spend below circa £1200 you can claim what you need to do your trip. We've seen BA pay up for ski equipment in this situation and you seem to be in a similar situation. It's very important to keep receipts, photograph them so you don't lose the receipts, photo the items, and photo your checked luggage whenever it finally gets delivered. Ensure you spend the minimum you need for your holiday, as if it was your own money, which I suppose it will be at this stage Though you may be somewhere isolated, pretty much all of France is on "next day" delivery services by various courier companies so it shouldn't be difficult.

I'm a bit surprised by the insurance company's response, that isn't really for this forum but I would follow up on that if you bought the cover thinking you would be covered.

In terms of tracking your items: just use the WorldTracer screens via BA.com - no-one will give you any better information, not that WT is terribly good. Keep the information updated, but then get on with your life, climbing all the way.