Holy cow Batman! (As Devin would say)
Yeah... that isn't going to work. Will the laptops that the teachers have support 11a? I'm guessing very few will, so I'll assume that going forward.
First, will they all be in one location, like an auditorium or spread around in different classrooms? Again, figuring you said you have three AP's, I'm guessing auditorium.
To serve Internet to 350 people simultaneously with three AP's isn't going to happen, but the real problem is if they are all in one location, the co-channel interference is the real issue.
Will the 120 series AP's form a mesh? If you mount more AP's, mount the low to the ground, like under tables and such. Why you ask? Well, the main problem is going to be co-channel interference so what you need is to block as much signal from same channel devices as possible. By mounting the AP's low, you are using the attenuation of people in your favor.
When is this conference? If they are adamant about having Wi-Fi service for all 350 teachers at once, it is going to be an interesting design to get it done. Feel free to contact me or post more questions on the forum so we can come to a solution.