Nice video.

I guess I have to ask, how much were you expecting to pay? You asked for 20 soles, did you ever get that rate?

From the airport to Miraflores I always pay 40 soles. I don't know if it is overpriced but what I do is call up one of the local cab companies (either Taxi Seguro or Taxi Real) one day before departure date and arrange the cab pick up. It requires an international call from the US (a few cents) and be fluent in Spanish. They will take your flight info, arrival time and a local cell phone number.The cab driver will usually call you up some minutes after landing to make sure you see each other upon exiting the arrivals hall.
If you travel frequently to Peru, getting a local cellphone is pretty easy and cheap.

Anyway, the cab driver waits for you with a sign with your name. Then he escorts you to his car in the parking lot, not far away from the curb. 40 soles may be too much (compared to what informal cabs charge outside the airport) but that way I avoid the interaction with the taxi mafia, which is a real agravation, even for someone fluent in spanish like me. Totally worth it. Payment of the fare is CASH upon arrival at the destination, no tips required, just the 40 soles arranged with the cab company.

PS. I am not sure if a local cellphone number is definitely required but if you don't have one, I think you could call the taxi company directly if you can't find the driver at the airport. Again, spansih fluency is highly recommended.