Highest capacity protected 18650 is AW's, 2200 mAh. Highest capacity unprotected is LG 2400 mAh, at batteryspace.com.
But the Pila recharger relies on the battery's protection circuit to interrupt the charging process. AW's batteries have an overcharge protection cut-off of 4.35 V, which is good to prevent the battery from going up in flames, but bad for the life of the battery.
I'd recommend the DSD lithium ion charger, which terminates the charge at 4.10 or 4.20 V. You can get the charger for around $10 from AW, Emil, Dae, or Lighthound. Emil has an optional automotive power adapter for the DSD charger.