It boils down to one thing: What do you want the discs to do? I will say one thing your bag layout looks golden as far as putters,upshots, midrange, pure distance and utility. You seem to have all the basis covered except those darn fairway drivers. Unfortunately they, in my opinion, are the most important. This thread is kinda neat because you and I are in the same boat as far as distance. So here we go. (This is my take on what you have)
I see a bit more distance potential and line shaping with the Eagles. They are a bit understable at high speeds which will give you that S-turn more often usually resulting in greater distance. What you sacrifice for this is a bit of unpredictability, especially with any kind of wind. When it flips it -will- come back the question that I ask will it come back soon enough to give me the end result I am looking for.
The Teebird has an all-around stable/straight flight path. In my opinion the consistency in flight is what makes it so popular. Stable enough that it won't flip too hard but easy to throw even at lower powers. The Teebird is my fairway of choice, I carry 3-5 at any one time varying in condition/weight/plastic.
I have yet to throw a TL but I have heard decent things about it. If you cannot control a Teebird the TL is the next disc you should try.
The fact of the matter is the 3 of them -do- overlap as far as distance. On a turnover the Eagle might nudge out the teebird while on a flat line the glide of a teebird might knock off the eagle. As far as line shaping for me that's a personal thing. A beat in teebird will shape lines for me, but maybe not for you. By the same token the Eagle might shape well for you but not for me. My suggestion is to take them all to a football field on a moderate wind day and give them a chuck. You will learn more about them that way I think
Best of luck.