Jesus didn't condemn public prayer. Jesus himself prayed publicly on occasion such as when he raised up Lazarus. What Jesus condemned was praying publicly for the purpose of impressing others with your righteousness.
1 Corinthians 14:16 refers to public prayer within the christian congregation as there is mention of one praying and others saying "amen" in response. So public prayer is scriptural.
But I still sympathize with your sentiments. I don't like public prayer either. It always smacks of an opportunity - no, a temptation - for the one praying to try to make or maintain a good impression with others. I can't help but think that the one praying will always be self conscious of what he is saying and trying to do a good job so as not to embarrass himself. It's only human for someone speaking before a crowd to exercise care that he speaks well and does not embarrass himself. This means that the one praying publicly can never give a 100% sincere prayer to God. He is always, in a sense, praying to the audience.
Also, aren't you not supposed to say the same things over and over?
Speaking of that, you will notice that every public pray-er seems to have his own mental prayer outline or prayer manuscript that he repeats when he has to pray. Again I believe the reason for this is pressure to make a good impression and not embarrass yourself publicly. That pressure tends to force the pray-er to develop a "safe" prayer that he can repeat every time without the risk of embarrassing himself if he were to be more spontaneous.
As a side note, if it is really true that it is wrong to repeat the same prayer by rote or from a prayer book whenever you pray, then how can it be acceptable to God to repeat the kingdom songs by rote or from a song book when you sing? Furthermore, it is a fact that the bible book of Psalms contains prayers that were written with Hebrew acrostics for the purpose of making them easy to remember for easy recitation. So why would God inspire psalmists to write prayer songs in a manner to make them easy to remember and recite if he does not approve of repeating prayers by memory?
JWs must be wrong about this teaching about not repeating the same prayer by rote. I believe the translation of Matthew 6 where it says not to say the same thing over and over again is actually an erroneous translation. The greek text actually says "do not multiply words". I believe this is referring to make very long, wordy prayers, thinking that God will consider you more spiritual if you talk to him for a very long time. The reason I say this is because elsewhere in the gospels Jesus also condemned the practice of making long prayers for a pretense.
In fact the very mistranslated verse in the NWT indicates that it is about the wordiness of the prayer and not about repeating the same prayer by rote when you pray:
"When praying, do not say the same things over and over again as the people of the nations do, for they imagine they will get a hearing for their use of many words" - Matthew 6:7
Did you see the phrase "their use of many words"? That phrase does not match the first part of the verse which is rendered as saying the same things over and over again. A person can have a short prayer with few words that he says by rote whenever he prays. So clearly its not about praying by rote when you pray. It's about having unnecessarily long, wordy prayers, imagining that the length of the prayer determines God's interest in it.