As you said, Mike, fasting was common in Jesus’ day, but Jesus’ teaching is a bit confusing to me.
First of all, who are the “hypocrites”? The Pharisees fasted on Mondays and Thursday, the weekdays when the Torah is read in the synagogue, but there is no outward sign for these fasts. If the disfigured face Jesus is referring to means a face unwashed accompanied by hair unoiled, the prohibition against washing and anointing is only found in regard to Yom Kippur, the most holy day of the Jewish year, and one on which all Jews fast. Could Jesus be downplaying Yom Kippur? And since the prohibition of washing and oiling one’s hair was applicable to everyone, are all Jews hypocrites?
It may be that Jesus is attacking fasting in general, though he himself fasted for forty days (Matthew 4:1-2). In the Gospel According to Mark (2: 18-20 NRSV) Jesus abolishes all fasting for his followers as long as he is alive: “The wedding guests cannot fast while the bridegroom is with them, can they? … The days will come when the bridegroom is taken away from them, and then they will fast on that day.” It sounds like Jesus is abolishing fasting as a practice with the exception of a fast on the day of his death. It is possible to read the text as meaning an annual fast on Good Friday or just a fast for his followers on the first Good Friday. According to the Didache (8:1) the early Christians followed the Pharisaic custom of fasting twice weekly, but did so on Wednesday and Friday to avoid being mistaken for Jews, but I couldn't find anything about fasting on Good Friday.
Your understanding of fasting as a means of shifting one’s focus from self to God makes sense, though the rabbis frowned on private fasting (Taanit 11a) as a way of repentance, and focused the meaning of fast days on the needs of the poor. Those who fast are obligated to give charity to the poor so that the poor would have enough money to eat well when the fast is over (Sanhedrin 35a).
It seems to me that Jesus is balancing his political teachings regarding justice to the poor with inward–focused practices bringing one closer to God. If so Jesus’ take on this particular practice is a departure from the rabbis who taught that fasting is not about getting right with God, but about doing right by the poor: “The merit of the fast day is in the amount of charity given to the poor” (Berachot 6b).