Lottery Analyst:
I am new here. So I did not see the post up to now. It is an initially good post. And I do not know very much about some of the information mentioned but I can't resist to make some comments.
To 1) I do not know the complete history of the Georgia Fantasy 5/39 but I would assume that we all would have heard about it if in that history two times in a row the same numbers were picked.
So my assumption would be - maybe up to now never any 5 numbers were drawn twice which would make this even better - that I would only need to buy 575.756 tickets to win the Georgia Fantasy Big Hit.
To 2) I think you forgot to mention that a) you are talking about the odds to win the big prize money and that b) if you are going for that prize the 10 tickets (or 100) should be different. If all of your tickets would be the same your chances are not necessarily increasing. In a jackpot scenario you might even have to share the prize money with yourself.
To 3) You are definitely right here, my opinion exactly; that you have to play with the focus on minimizing your losses, that is what I call it. You need to win some smaller prices to increase the number of sets you can play to - dventually - have a big hit.
To 4 and 5) Quick picks - even though I played them too - they have still a bad taste to them. Why would I ask the company that is performing the Lottery what numbers to pick? That seems strange to me, and I never got over that. Imagine: I give you $10 dollars if you guessed the number between 1 and 10 that I thought off, and you ask me what number you should pick. I can assure you that you do not win $10 in that case.
To 6) I do not know the terminology used in your grouping. I like your grouping. It seems to make sense. I designed many programs to "predict" numbers, to "wheel" numbers and such. I never liked programs that make me decide to much myself. After all if you want a "tool" rather than a "system" that would be fine, but you are expecting a system that would be different.
I personally went away from programs creating numbers, I am still working on it, but it is not that interesting any longer. Now I see forecasts using only a "short-term" history "memory" as the most likely "systems" to succeed. There also has to be a certain "chance" or "randomness" built into the "system". Why? Well, you are trying to challenge "randomness" (or potential "randomness") so you should fight it with its own weapon. I have success with these kinds of systems. Success once again meaning: "Minimizing the losses!" to have more chances to hit the "Big Win" dventually.
That was long and probably boring, and I did not check it. I hope it brings over my points somewhat.
Thanks for your time.