I think it can be very easily done

OK, I think I can do it. I just asked the staff outside as a check and I think I can get an overnight bus tomorrow to Arequipa. So on Tuesday morning I can be in Arequipa. I stay there Tuesday night, Wednesday during the day (let's say) I get a bus to Tacna, which is about five or six hours. Playing it safe, let's say I stay Wednesday night in Tacna. Tacna is about two hours from Arica in Chile, I can cross over on Thursday and if necessary spend Thursday night in Arica. I then have about five days to get from there to Santiago. If I am allowed to buy a cheap air ticket (I have sent an e-mail in mangled Spanish enquiring) from Arica to Santiago I am sorted, and will have a few days in Arica. If not, under normal circumstances there are loads of direct buses from Arica to Santiago taking about 30h, which I'd rather not do but needs must. In any event, I have nearly five days. If I can't get the flight but the buses are OK I can do two bus journeys, breaking somewhere in mid-northern Chile. I also get Tuesday (all day and evening) and Wednesday afternoon in Tacna to see a little bit of these places en route.

I wish I could be more confident about getting down from Arica to Santiago, but this seems vaguely plausible. My guide book suggests it's best to get a taxi collective across the border, which sounds a bit involved but I am sure there will be some decent-ish option.

Now I just have to convince myself emotionally that it's all OK and I can relax. :-)