First of all, what will your number be without those seniors? Is it 27 or is it less? It changes your recruiting if you're closer to capacity. You may want to ask the applicants to submit some sort of application, in varying degrees of complexity (it could be anywhere from a paragraph as to why they want to be on the team to a full-blown application). The alternative is to accept anyone on the team that wants to join, coupled with the truth that not everyone will go to Atlanta...but I suggest that this would need some sort of evaluation process implemented.
And from how I understand it, it's not that you want to deprive anyone of the experience, but it's more of dealing with the issue that you can only provide for 35 at this moment in time and you want to give that to the students who are more likely to get more out of it (assuming that the people who put in the most work is because they are the most interested). Just to clarify, in "providing" for a student, does that mean they go for free? Or does this team they are allowed to go, but still have to fork over some money at the end? That changes things as well
There are many ways that you can "weed" out students. I've heard of point systems, report cards, 360-degree analyses, and the like. But in the end, it's all about using what's best for your team. With these seniors, are you losing a lot of your student leadership/management? Do you have a student/some students in place for when the seniors leave, or is it unnecessary? I'd love to know more about your team's specific structure. Which system will work best will depend on the time that the management can put in to compile the results.
Mind you, you may not find that thing that works best on the first try...it may take multiple instances before something really sticks. So just like the robot, don't be afraid of trial and error when it comes to managing your team!
I know there's a lot of variables, and I'm not answering much in this post, but it can be worked out pretty quickly with some brainstorming. Please PM me if you'd like to talk more about this.
Good luck!
-Jessica B