Perhaps it might be best to take a step back and decide what the goals are, as well as some of the issues, especially how it affects those that Scale is serving..
You can keep track of the inventory with paper and pencil faster than scanning a badge. Marking a badge would take longer and be harder. Is trust really an issue with the shirts since now there are those who want to give them away and how many people would really take more than one, especially if you let them know after a given time they can come back for more.
While it is nice to encourage people to the expo floor, forcing them to go in order to get the shirt seems much like treating them like cattle. It is also wasting their time, which I personally think is unacceptable. Also, there is limited times in which the expo floor is open, which limits when people can go and it also means that a person who only makes it on Thursday does not get a shirt.
From what I heard the reason for the booth was because the shirts did not arrive in time,
To me, the reduction in shirts given out screams that there was a problem, unless the goal is to save money by not giving out shirts.
As a side note, I personally would NOT donate any of the old shirts to Goodwill. This is for many reasons, such as they are just going to try to sell them. If you want to do good with the shirts, then donate them to a place like the Battered Women's Shelter or organizations which will give them to those in need.