This entire series used to be one large study. A internet-met brother (like you) in Houston, Mike Chambers, led his home-church in this series and then upon visiting us later in San Jose said it had taken 6 weeks to get through all the material. So I went back and broke it up into six studies, later expanding it to seven.
The real meat of it is the first study, the Lord's Prayer done r-e-a-l--s-l-o-w. Each phrase is to be savored and understood before moving on. Scripture expansions and meditation are the methodology suggested, as embedded in the Study.
Specifically, I would make Study 1 (the prayer outline) center stage for all 7 (or whatever subset you decide to do) weeks. For example, ask people to commit on a temporary basis to pray every day through this, dedicating 1/2 or 1 hour of time. Then ask them every week what further insights they have gleaned from the Holy Spirit about any particular element or aspect. After this, for the rest of the time of the meeting go through the new material. This sets the pace for people to think of what to bring to the table the following week to help keep them faithful to the regimen of prayer for a season.
As to how to introduce the first study, I think it best to hit them cold, letting them do homework afterwards as real prayer and study for the follow-up sessions. If you want to salt them in advance of Study 1, ask them to meditate on Jesus' question in the garden to His disciples: "Could you not tarry one hour?" and to think of reasons why not, and what could have helped them, and what the spiritual consequences of failure in prayer were back then for them. Then offer the Study as the answer to the question--as a framework for really being able to "tarry one hour" with the Lord--by using His outline as a discipline and guide to keep our thoughts corralled towards Him.
As to style, I have done Study 1 as just a regular Bible Study (originally) and last year at a downtown meeting at The DOOR. But I think it best done in a spirit of prayer, where the whole meeting becomes a group prayer and people can learn from example how to flow in and out of prayer without a lot of "amens" and other hoopla--for prayer is an attitude of the heart that is quite distinct in spirit. Everyone is able to tell when you are just talking and when you are addressing the Holy One. You have to feel comfortable with this, or it might come off as strange, but I think making this a bible guided "prayer meeting" rather than a "bible study" is the best approach. Just a suggestion.
One of the most lively and fun sections is the "Scripture Praying" technique (the added seventh study, put into position 6). After introducing it and going through the examples, ask people to take some verses and try it aloud; again in a SPIRIT of true prayer, addressing God directly. What a great way to pray "in accordance with His will", by actually using His word to do it!
I hope that God will use this series to make more clear to you the "mystery of godliness", which is Christ in you, the hope of glory. When insights pierce through you (and there are many thousands) from the body, and you realize you are not alone in pining for and worshiping our God, it is sweet indeed! If we were to put in all the insights people have gleaned and shared from the Lord's prayer, it would surely fill the internet. The ones listed are merely "springboard" ideas, so really encourage participation in these studies. Give people time to think of things and look them up. Let there be silence for a minute or two while people think. Without such participation, these studies are all too short.