Thanks Bill. Maybe there was something different, or maybe something has changed (I'm hoping the latter). Algadones Optical sent my frames to San Diego and they arrived in the mail 10 days later. I went to 5 or 6 opticians in Algadones the same day, and they all said the same thing, i.e. that the local lab couldn't do polycarbonate, and it would take 1-2 weeks.
One data point - a couple of years ago I bought two pairs of glasses from Algadones Optical and specifically asked for polycarbonate. Picked them up 2 hours later. Next time in Algadones, I visited the same store and, when the optician looked at my glasses, he very clearly said "These are not polycarbonate; If you want polycarbonate for the replacement lenses, they have to be sent to San Diego". They turned up 10 days later.
I'm hoping something changed, and that the local lab can now do polycarbonate; I don't feel comfortable about not being able to check out the prescription before leaving the store.